Chapter Resource Masters
CNSUMABLE WRKBKS Man of the worksheets contained in the Chapter Resource Masters booklets are available as consumable workbooks in both English and Spanish. Stud Guide and Intervention Workbook 0-0-- Stud Guide and Intervention Workbook (Spanish) 0-0--X Skills Practice Workbook 0-0-- Skills Practice Workbook (Spanish) 0-0-9- Practice Workbook 0-0-- Practice Workbook (Spanish) 0-0-0- Reading to Learn Mathematics Workbook 0-0-00- ANSWERS FR WRKBKS The answers for Chapter of these workbooks can be found in the back of this Chapter Resource Masters booklet. StudentWorks This CD-RM includes the entire Student Edition tet along with the English workbooks listed above. TeacherWorks All of the materials found in this booklet are included for viewing and printing in the Glencoe Algebra TeacherWorks CD-RM. Glencoe/McGraw-Hill Copright b The McGraw-Hill Companies, Inc. All rights reserved. Printed in the United States of America. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced onl for classroom use; be provided to students, teachers, and families without charge; and be used solel in conjunction with Glencoe Algebra. An other reproduction, for use or sale, is prohibited without prior written permission of the publisher. Send all inquiries to: The McGraw-Hill Companies rion Place Columbus, H 0-0 ISBN: 0-0--0 Glencoe Algebra Chapter Resource Masters 9 0 0 0 09 0 0 0 0 0 0
Contents Vocabular Builder................ vii Lesson - Stud Guide and Intervention........ 0 0 Skills Practice....................... 0 Practice........................... 0 Reading to Learn Mathematics.......... 0 Enrichment......................... 0 Lesson - Stud Guide and Intervention........ 09 0 Skills Practice....................... Practice........................... Reading to Learn Mathematics.......... Enrichment......................... Lesson - Stud Guide and Intervention........ Skills Practice....................... Practice........................... Reading to Learn Mathematics.......... 9 Enrichment......................... 0 Lesson - Stud Guide and Intervention........ Skills Practice....................... Practice........................... Reading to Learn Mathematics.......... Enrichment......................... Lesson - Stud Guide and Intervention........ Skills Practice....................... 9 Practice........................... 0 Reading to Learn Mathematics.......... Enrichment......................... Chapter Assessment Chapter Test, Form............ Chapter Test, Form A........... Chapter Test, Form B........... Chapter Test, Form C........... 9 0 Chapter Test, Form D........... Chapter Test, Form............ Chapter pen-ended Assessment...... Chapter Vocabular Test/Review....... Chapter Quizzes &............... Chapter Quizzes &............... Chapter Mid-Chapter Test............ 9 Chapter Cumulative Review........... 0 Chapter Standardized Test Practice.. Unit Test/Review (Ch. )........ Standardized Test Practice Student Recording Sheet.............. A ANSWERS...................... A A Glencoe/McGraw-Hill iii Glencoe Algebra
Teacher s Guide to Using the Chapter Resource Masters The Fast File Chapter Resource sstem allows ou to convenientl file the resources ou use most often. The Chapter Resource Masters includes the core materials needed for Chapter. These materials include worksheets, etensions, and assessment options. The answers for these pages appear at the back of this booklet. All of the materials found in this booklet are included for viewing and printing in the Algebra TeacherWorks CD-RM. Vocabular Builder Pages vii viii include a student stud tool that presents up to twent of the ke vocabular terms from the chapter. Students are to record definitions and/or eamples for each term. You ma suggest that students highlight or star the terms with which the are not familiar. WHEN T USE Give these pages to students before beginning Lesson -. Encourage them to add these pages to their Algebra Stud Notebook. Remind them to add definitions and eamples as the complete each lesson. Stud Guide and Intervention Each lesson in Algebra addresses two objectives. There is one Stud Guide and Intervention master for each objective. WHEN T USE Use these masters as reteaching activities for students who need additional reinforcement. These pages can also be used in conjunction with the Student Edition as an instructional tool for students who have been absent. Skills Practice There is one master for each lesson. These provide computational practice at a basic level. WHEN T USE These masters can be used with students who have weaker mathematics backgrounds or need additional reinforcement. Practice There is one master for each lesson. These problems more closel follow the structure of the Practice and Appl section of the Student Edition eercises. These eercises are of average difficult. WHEN T USE These provide additional practice options or ma be used as homework for second da teaching of the lesson. Reading to Learn Mathematics ne master is included for each lesson. The first section of each master asks questions about the opening paragraph of the lesson in the Student Edition. Additional questions ask students to interpret the contet of and relationships among terms in the lesson. Finall, students are asked to summarize what the have learned using various representation techniques. WHEN T USE This master can be used as a stud tool when presenting the lesson or as an informal reading assessment after presenting the lesson. It is also a helpful tool for ELL (English Language Learner) students. Enrichment There is one etension master for each lesson. These activities ma etend the concepts in the lesson, offer an historical or multicultural look at the concepts, or widen students perspectives on the mathematics the are learning. These are not written eclusivel for honors students, but are accessible for use with all levels of students. WHEN T USE These ma be used as etra credit, short-term projects, or as activities for das when class periods are shortened. Glencoe/McGraw-Hill iv Glencoe Algebra
Assessment ptions The assessment masters in the Chapter Resources Masters offer a wide range of assessment tools for intermediate and final assessment. The following lists describe each assessment master and its intended use. Chapter Assessment CHAPTER TESTS Form contains multiple-choice questions and is intended for use with basic level students. Forms A and B contain multiple-choice questions aimed at the average level student. These tests are similar in format to offer comparable testing situations. Forms C and D are composed of freeresponse questions aimed at the average level student. These tests are similar in format to offer comparable testing situations. Grids with aes are provided for questions assessing graphing skills. Form is an advanced level test with free-response questions. Grids without aes are provided for questions assessing graphing skills. All of the above tests include a freeresponse Bonus question. The pen-ended Assessment includes performance assessment tasks that are suitable for all students. A scoring rubric is included for evaluation guidelines. Sample answers are provided for assessment. A Vocabular Test, suitable for all students, includes a list of the vocabular words in the chapter and ten questions assessing students knowledge of those terms. This can also be used in conjunction with one of the chapter tests or as a review worksheet. Intermediate Assessment Four free-response quizzes are included to offer assessment at appropriate intervals in the chapter. A Mid-Chapter Test provides an option to assess the first half of the chapter. It is composed of both multiple-choice and free-response questions. Continuing Assessment The Cumulative Review provides students an opportunit to reinforce and retain skills as the proceed through their stud of Algebra. It can also be used as a test. This master includes free-response questions. The Standardized Test Practice offers continuing review of algebra concepts in various formats, which ma appear on the standardized tests that the ma encounter. This practice includes multiplechoice, grid-in, and quantitativecomparison questions. Bubble-in and grid-in answer sections are provided on the master. Answers Page A is an answer sheet for the Standardized Test Practice questions that appear in the Student Edition on pages 0 0. This improves students familiarit with the answer formats the ma encounter in test taking. The answers for the lesson-b-lesson masters are provided as reduced pages with answers appearing in red. Full-size answer kes are provided for the assessment masters in this booklet. Glencoe/McGraw-Hill v Glencoe Algebra
NAME DATE PERID Reading to Learn Mathematics Vocabular Builder This is an alphabetical list of the ke vocabular terms ou will learn in Chapter. As ou stud the chapter, complete each term s definition or description. Remember to add the page number where ou found the term. Add these pages to our Algebra Stud Notebook to review vocabular at the end of the chapter. consistent Vocabular Term Found on Page Definition/Description/Eample Vocabular Builder kuhn SIHS tuhnt dependent elimination ih LIH muh NAY shuhn independent inconsistent (continued on the net page) Glencoe/McGraw-Hill vii Glencoe Algebra
NAME DATE PERID Reading to Learn Mathematics Vocabular Builder (continued) Vocabular Term substitution SUHB stuh T shuhn Found on Page Definition/Description/Eample sstem of equations sstem of inequalities Glencoe/McGraw-Hill viii Glencoe Algebra
- NAME DATE PERID Stud Guide and Intervention Graphing Sstems of Equations Number of Solutions Two or more linear equations involving the same variables form a sstem of equations. A solution of the sstem of equations is an ordered pair of numbers that satisfies both equations. The table below summarizes information about sstems of linear equations. Graph of a Sstem intersecting lines same line parallel lines Number of Solutions eactl one solution infinitel man solutions no solution consistent and consistent and Terminolog inconsistent independent dependent Lesson - Eample Use the graph at the right to determine whether the sstem has no solution, one solution, or infinitel man solutions. a. Since the graphs of and intersect, there is one solution. b. Since the graphs of and are parallel, there are no solutions. c. Since the graphs of and coincide, there are infinitel man solutions. Eercises Use the graph at the right to determine whether each sstem has no solution, one solution, or infinitel man solutions..... Glencoe/McGraw-Hill 0 Glencoe Algebra
- Solve b Graphing ne method of solving a sstem of equations is to graph the equations on the same coordinate plane. Eample Graph each sstem of equations. Then determine whether the sstem has no solution, one solution, or infinitel man solutions. If the sstem has one solution, name it. a. The graphs intersect. Therefore, there is one solution. The point (, ) seems to lie on both lines. Check this estimate b replacing with and with in each equation. ( ) ( ) or The solution is (, ). b. The graphs coincide. Therefore there are infinitel man solutions. Eercises Graph each sstem of equations. Then determine whether the sstem has no solution, one solution, or infinitel man solutions. If the sstem has one solution, name it.... NAME DATE PERID (, ) Stud Guide and Intervention (continued) Graphing Sstems of Equations (, ) (, ) (, )... (, ) Glencoe/McGraw-Hill 0 Glencoe Algebra
- NAME DATE PERID Skills Practice Graphing Sstems of Equations Use the graph at the right to determine whether each sstem has no solution, one solution, or infinitel man solutions..... Graph each sstem of equations. Then determine whether the sstem has no solution, one solution, or infinitel man solutions. If the sstem has one solution, name it.... (, ) Lesson - (, ). 9. 0. (, 0) (, )... (, 0) Glencoe/McGraw-Hill 0 Glencoe Algebra
- Use the graph at the right to determine whether each sstem has no solution, one solution, or infinitel man solutions..... Graph each sstem of equations. Then determine whether the sstem has no solution, one solution, or infinitel man solutions. If the sstem has one solution, name it.... 0 NAME DATE PERID Practice Graphing Sstems of Equations 0 (, ) BUSINESS For Eercises and 9, use the following information. Nick plans to start a home-based business producing and selling gourmet dog treats. He figures it will cost $0 in operating costs per week plus $0.0 to produce each treat. He plans to sell each treat for $.0.. Graph the sstem of equations 0. 0 and. to represent the situation. 9. How man treats does Nick need to sell per week to break even? Cost ($) 0 0 0 0 0 Dog Treats (0, 0) 0. 0. 0 0 0 0 Sales ($) SALES For Eercises 0, use the following information. A used book store also started selling used CDs and videos. In the first week, the store sold 0 used CDs and videos, at $.00 per CD and $.00 per video. The sales for both CDs and videos totaled $0.00 0. Write a sstem of equations to represent the situation.. Graph the sstem of equations.. How man CDs and videos did the store sell in the first week? c v 0 c v 0 (0, 0) Glencoe/McGraw-Hill 0 Glencoe Algebra
- NAME DATE PERID Reading to Learn Mathematics Graphing Sstems of Equations Pre-Activit How can ou use graphs to compare the sales of two products? Read the introduction to Lesson - at the top of page 9 in our tetbook. What is meant b the term linear function? What does it mean to sa that two lines intersect? Reading the Lesson. Each figure shows the graph of a sstem of two equations. Write the letter of the figures that illustrate each statement. Lesson - A. B. C. D. a. A sstem of two linear equations can have an infinite number of solutions. b. A sstem of equations is consistent if there is at least one ordered pair that satisfies both equations. c. If two graphs are parallel, there are no ordered pairs that satisf both equations. d. If a sstem of equations has eactl one solution, it is independent. e. If a sstem of equations has an infinite number of solutions, it is dependent. Helping You Remember. Describe how ou can solve a sstem of equations b graphing. Glencoe/McGraw-Hill 0 Glencoe Algebra
- NAME DATE PERID Enrichment Graphing a Trip The distance formula, d rt, is used to solve man tpes of problems. If ou graph an equation such as d 0t, the graph is a model for a car going at 0 mi/h. The time the car travels is t; the distance in miles the car covers is d. The slope of the line is the speed. Suppose ou drive to a nearb town and return. You average 0 mi/h on the trip out but onl mi/h on the trip home. The round trip takes hours. How far awa is the town? 0 d slope is 0 slope is t The graph at the right represents our trip. Notice that the return trip is shown with a negative slope because ou are driving in the opposite direction. Solve each problem.. Estimate the answer to the problem in the above eample. About how far awa is the town?. Graph this trip and solve the problem. An airplane has enough fuel for hours of safe fling. n the trip out the pilot averages 00 mi/h fling against a headwind. n the trip back, the pilot averages 0 mi/h. How long a trip out can the pilot make? d 00 t. Graph this trip and solve the. Graph this trip and solve the problem. You problem. You drive to a town drive at an average speed of 0 mi/h to a 00 miles awa. n the trip out ou discount shopping plaza, spend hours average mi/h. n the trip back ou shopping, and then return at an average average 0 mi/h. How man hours do speed of mi/h. The entire trip takes ou spend driving? hours. How far awa is the shopping plaza? d d 0 0 t t Glencoe/McGraw-Hill 0 Glencoe Algebra
- NAME DATE PERID Stud Guide and Intervention Substitution Substitution ne method of solving sstems of equations is substitution. Eample Eample Use substitution to solve the sstem of equations. Substitute for in the second equation. Second equation Combine like terms. Divide each side b. Simplif. Use to find the value of. First equation ( ) Simplif. The solution is (, ). Solve for one variable, then substitute. Solve the first equation for since the coefficient of is. First equation Subtract from each side. Simplif. Find the value of b substituting for in the second equation. Second equation ( ) Distributive Propert 0 Combine like terms. 0 Subtract from each side. 0 0 Simplif. 0 0 0 0 Divide each side b 0. Use to find the value of. () The solution is (, ). Simplif. Lesson - Eercises Use substitution to solve each sstem of equations. If the sstem does not have eactl one solution, state whether it has no solution or infinitel man solutions...... c d. 0 c d. b a. 9. a b 0... 0. 0. 0. 0. 0 0.. Glencoe/McGraw-Hill 09 Glencoe Algebra
- Real-World Problems Substitution can also be used to solve real-world problems involving sstems of equations. It ma be helpful to use tables, charts, diagrams, or graphs to help ou organize data. Eample CHEMISTRY How much of a 0% saline solution should be mied with a 0% saline solution to obtain 000 milliliters of a % saline solution? Let s the number of milliliters of 0% saline solution. Let t the number of milliliters of 0% saline solution. Use a table to organize the information. 0% saline 0% saline % saline Total milliliters s t 000 Milliliters of saline 0.0s 0.0t 0.(000) Write a sstem of equations. s t 000 0.0s 0.0t 0.(000) Use substitution to solve this sstem. s t 000 First equation s 000 t Solve for s. 0.0s 0.0t 0.(000) Second equation 0.0(000 t) 0.0t 0.(000) s 000 t 00 0.0t 0.0t 0.(000) Distributive Propert 00 0.0t 0.(000) Combine like terms. 0.0t 0 Simplif. 0.0t 0 0.0 0.0 Divide each side b 0.0. t 00 Simplif. s t 000 First equation s 00 000 t 00 s 00 Solve for s. 00 milliliters of 0% solution and 00 milliliters of 0% solution should be used. Eercises NAME DATE PERID Stud Guide and Intervention (continued) Substitution. SPRTS At the end of the 000-00 football season, Super Bowl games had been plaed with the current two football leagues, the American Football Conference (AFC) and the National Football Conference (NFC). The NFC won five more games than the AFC. How man games did each conference win? Source: New York Times Almanac. CHEMISTRY A lab needs to make 00 gallons of an % acid solution b miing a % acid solution with a 0% solution. How man gallons of each solution are needed?. GEMETRY The perimeter of a triangle is inches. The longest side is inches longer than the shortest side, and the shortest side is three-fourths the length of the middle side. Find the length of each side of the triangle. Glencoe/McGraw-Hill 0 Glencoe Algebra
- NAME DATE PERID Skills Practice Substitution Use substitution to solve each sstem of equations. If the sstem does not have eactl one solution, state whether it has no solution or infinitel man solutions..... 0.... 9. 0. Lesson -.... 9 9. 0. 0 0.. 9. 0.. 0 Glencoe/McGraw-Hill Glencoe Algebra
- NAME DATE PERID Practice Substitution Use substitution to solve each sstem of equations. If the sstem does not have eactl one solution, state whether it has no solution or infinitel man solutions.... 0..... 9. 0... 0. 0. 0.. 0........ EMPLYMENT For Eercises 9, use the following information. Kenisha sells athletic shoes part-time at a department store. She can earn either $00 per month plus a % commission on her total sales, or $00 per month plus a % commission on total sales. 9. Write a sstem of equations to represent the situation. 0. What is the total price of the athletic shoes Kenisha needs to sell to earn the same income from each pa scale?. Which is the better offer? MVIE TICKETS For Eercises and, use the following information. Tickets to a movie cost $. for adults and $.0 for students. A group of friends purchased tickets for $... Write a sstem of equations to represent the situation.. How man adult tickets and student tickets were purchased? Glencoe/McGraw-Hill Glencoe Algebra
- NAME DATE PERID Reading to Learn Mathematics Substitution Pre-Activit How can a sstem of equations be used to predict media use? Read the introduction to Lesson - at the top of page in our tetbook. What is the sstem of equations? Based on the graph, are there 0,, or infinitel man solutions of the sstem? Reading the Lesson. Describe how ou would use substitution to solve each sstem of equations. a. b. c. Lesson - d.. Jess solved a sstem of equations and her result was. All of her work was correct. Describe the graph of the sstem. Eplain.. Miguel solved a sstem of equations and his result was. All of his work was correct. Describe the graph of the sstem. Eplain. Helping You Remember. What is usuall the first step in solving a sstem of equations b substitution? Glencoe/McGraw-Hill Glencoe Algebra
- NAME DATE PERID Enrichment Equations of Lines and Planes in Intercept Form ne form that a linear equation ma take is intercept form. The constants a and b are the - and -intercepts of the graph. a b z In three-dimensional space, the equation of a plane takes a similar form. a z b c Here, the constants a, b, and c are the points where the plane meets the,, and z-aes. z Solve each problem. z. Graph the equation. z. For the plane in Eercise, write an equation for the line where the plane intersects the -plane. Use intercept forms.. Write an equation for the line where the plane intersects the z-plane. z z. Graph the equation. z. Write an equation for the line where the plane intersects the z-plane. z. Write an equation for the -plane. z 0. Write an equation for the z-plane. 0. Write an equation for a plane parallel to the -plane with a z-intercept of. z 9. Write an equation for a plane parallel to the z-plane with an -intercept of. Glencoe/McGraw-Hill Glencoe Algebra
- NAME DATE PERID Stud Guide and Intervention Elimination Using Addition and Subtraction Elimination Using Addition In sstems of equations in which the coefficients of the or terms are additive inverses, solve the sstem b adding the equations. Because one of the variables is eliminated, this method is called elimination. Eample Eample Use addition to solve the sstem of equations. 9 Write the equations in column form and add to eliminate. ( ) 9 Solve for. Substitute for in either equation and solve for. The solution is (, ). Eercises Use elimination to solve each sstem of equations. The sum of two numbers is 0 and their difference is. Find the numbers. Let represent one number and represent the other number. 0 ( ) 9 9 Substitute for in either equation. 0 0 The numbers are and. Lesson -.. m n. a b 9 m n a b 0.. c d. 9 c d.. 9. 0.. 0. 0.. 0. 0. 0.9 0.. 0. 0. 0.. Rema is older than Ken. The difference of their ages is and the sum of their ages is 0. Find the age of each.. The sum of the digits of a two-digit number is. The difference of the digits is. Find the number if the units digit is larger than the tens digit. Glencoe/McGraw-Hill Glencoe Algebra
NAME DATE PERID Stud Guide and Intervention (continued) Elimination Using Addition and Subtraction Elimination Using Subtraction In sstems of equations where the coefficients of the or terms are the same, solve the sstem b subtracting the equations. Use subtraction to solve the sstem of equations. Write the equations in column form and subtract. ( ) Subtract the two equations. is eliminated. Divide each side b. Simplif. () Substitute for in either equation. Simplif. Subtract from each side. 9 9 The solution is (, ). Simplif. Divide each side b. Simplif. Use elimination to solve each sstem of equations... m n. a b 0 m n a b.. c d. c d. a b. 9. s t a b 0 s t 0.... 0. 0. 9 0... The sum of two numbers is 0. ne number is ten more than twice the other number. Find the numbers.. GEMETRY Two angles are supplementar. The measure of one angle is 0 more than three times the other. Find the measure of each angle. Glencoe/McGraw-Hill Glencoe Algebra
- NAME DATE PERID Skills Practice Elimination Using Addition and Subtraction Use elimination to solve each sstem of equations...... 9.. a b. c d a b c d 9. 9 0. 0. m n. m n.. 9. m n. m n Lesson -. The sum of two numbers is and their difference is. What are the numbers?. Find the two numbers whose sum is 9 and whose difference is. 9. The sum of two numbers is and their difference is. What are the numbers? 0. Find the two numbers whose sum is and whose difference is.. Two times a number added to another number is. Three times the first number minus the other number is 0. Find the numbers. Glencoe/McGraw-Hill Glencoe Algebra
- NAME DATE PERID Practice Elimination Using Addition and Subtraction Use elimination to solve each sstem of equations... p q. 9 p q..... 9 9. c d c d 0..... 9. 0... 0.. 0.. m n...9 m n. a b.. a b 0 9 9. The sum of two numbers is and their difference is. What are the numbers? 0. Four times one number added to another number is. Three times the first number minus the other number is 0. Find the numbers.. ne number added to three times another number is. Five times the first number added to three times the other number is. Find the numbers.. LANGUAGES English is spoken as the first or primar language in more countries than Farsi is spoken as the first language. Together, English and Farsi are spoken as a first language in 0 countries. In how man countries is English spoken as the first language? In how man countries is Farsi spoken as the first language?. DISCUNTS At a sale on winter clothing, Cod bought two pairs of gloves and four hats for $.00. Tori bought two pairs of gloves and two hats for $0.00. What were the prices for the gloves and hats? Glencoe/McGraw-Hill Glencoe Algebra
- NAME DATE PERID Reading to Learn Mathematics Elimination Using Addition and Subtraction Pre-Activit How can ou use a sstem of equations to solve problems about weather? Read the introduction to Lesson - at the top of page in our tetbook. What fact eplains wh the variable d gets eliminated from the sstem of equations? Reading the Lesson. Write addition or subtraction to tell which operation it would be easiest to use to eliminate a variable of the sstem. Eplain our choice. Sstem of Equations peration Eplanation a. b. c. 9 d. 9 Lesson - Helping You Remember. Tell how ou can decide whether to use addition or subtraction to eliminate a variable in a sstem of equations. Glencoe/McGraw-Hill 9 Glencoe Algebra
- NAME DATE PERID Enrichment Rózsa Péter Rózsa Péter (90 9) was a Hungarian mathematician dedicated to teaching others about mathematics. As professor of mathematics at a teachers college in Budapest, she wrote several mathematics tetbooks and championed reforms in the teaching of mathematics. In 9 she wrote Plaing with Infinit: Mathematical Eplorations and Ecursions, a popular work in which she attempted to conve the spirit of mathematics to the general public. B far Péter s greatest contribution to mathematics was her pioneering research in the field of recursive function theor. When ou evaluate a function recursivel, ou begin with one initial value of. Working from this single number, ou can use the function to generate an entire sequence of numbers. For instance, here is how ou use an initial value of to evaluate the function f() recursivel. f() () f() () 9 f(9) (9) f() () f() () The first five numbers of the sequence generated b this function are, 9,,, and. Write the first five numbers of the sequence generated b each function, using the given number as the initial value of.. f() ;. g() ;. f() ;. f() ;. h() ;. k() ; 0 Glencoe/McGraw-Hill 0 Glencoe Algebra
- NAME DATE PERID Stud Guide and Intervention Elimination Using Multiplication Elimination Using Multiplication Some sstems of equations cannot be solved simpl b adding or subtracting the equations. In such cases, one or both equations must first be multiplied b a number before the sstem can be solved b elimination. Eample Eample Use elimination to solve the sstem of equations. 0 If ou multipl the second equation b, ou can eliminate the terms. 0 ( ) 0 0 Substitute for in either equation. 0 0 0 0 0 0 The solution is, Eercises. Use elimination to solve each sstem of equations. Use elimination to solve the sstem of equations. 0 If ou multipl the first equation b and the second equation b, ou can eliminate the terms. ( ) 0 Substitute for in either equation. ( ) The solution is (, )... m n. a b m n a b.. c d. 0 c d 0 0. s t 9. a b 9. s t a b 0 0..... Lesson -. GARDENING The length of Sall s garden is meters greater than times the width. The perimeter of her garden is meters. What are the dimensions of Sall s garden?. Anita is ears older than Basilio. Three times Anita s age added to si times Basilio s age is. How old are Anita and Basilio? Glencoe/McGraw-Hill Glencoe Algebra
- NAME DATE PERID Stud Guide and Intervention (continued) Elimination Using Multiplication Determine the Best Method The methods to use for solving sstems of linear equations are summarized in the table below. Method Graphing Substitution Elimination Using Addition Elimination Using Subtraction Elimination Using Multiplication The Best Time to Use to estimate the solution, since graphing usuall does not give an eact solution if one of the variables in either equation has a coefficient of or if one of the variables has opposite coefficients in the two equations if one of the variables has the same coefficient in the two equations if none of the coefficients are or and neither of the variables can be eliminated b simpl adding or subtracting the equations Eample Determine the best method to solve the sstem of equations. Then solve the sstem. 0 Since the coefficients of will be additive inverses of each other if ou multipl the second equation b, use elimination. 0 ( ) 0 Substitute for in ( ) Multipl the second equation b. either equation. 0 Simplif. Eercises The solution is (, ). Add the two equations. is eliminated. Divide each side b. Simplif. 0 Add to each side. Simplif. Divide each side b. Simplif. Determine the best method to solve each sstem of equations. Then solve the sstem... m n. a b m n a b.. c d. 9 c d. 0. 9. s t 0 s t 0. a b 0. 0. a b 0 0 Glencoe/McGraw-Hill Glencoe Algebra
- NAME DATE PERID Skills Practice Elimination Using Multiplication Use elimination to solve each sstem of equations.. 9. 9.... 0. 0. 9. 0... 0 9. Two times a number plus three times another number equals. The sum of the two numbers is. What are the numbers?. Four times a number minus twice another number is. The sum of the two numbers is. Find the numbers. Determine the best method to solve each sstem of equations. Then solve the sstem.. 0. Lesson -.. 9. 0. Glencoe/McGraw-Hill Glencoe Algebra
- NAME DATE PERID Practice Elimination Using Multiplication Use elimination to solve each sstem of equations... 0... 9. 0.. 0. 0. 9. 0. 0 0. Eight times a number plus five times another number is. The sum of the two numbers is. What are the numbers?. Two times a number plus three times another number equals. Three times the first number plus four times the other number is. Find the numbers. Determine the best method to solve each sstem of equations. Then solve the sstem.... 0... 9. FINANCE Gunther invested $0,000 in two mutual funds. ne of the funds rose % in one ear, and the other rose 9% in one ear. If Gunther s investment rose a total of $ in one ear, how much did he invest in each mutual fund? 9. CANEING Laura and Brent paddled a canoe miles upstream in four hours. The return trip took three hours. Find the rate at which Laura and Brent paddled the canoe in still water. 0. NUMBER THERY The sum of the digits of a two-digit number is. If the digits are reversed, the new number is more than the original number. Find the number. Glencoe/McGraw-Hill Glencoe Algebra
- NAME DATE PERID Reading to Learn Mathematics Elimination Using Multiplication Pre-Activit How can a manager use a sstem of equations to plan emploee time? Read the introduction to Lesson - at the top of page in our tetbook. Can the sstem of equations be solved b elimination with addition or subtraction? Eplain. Reading the Lesson. Could elimination b multiplication be used to solve the sstem shown below? Eplain.. Tell whether it would be easiest to use substitution, elimination b addition, elimination b subtraction, or elimination b multiplication to solve the sstem. Eplain our choice. Sstem of Equations Solution Method Eplanation a. 0 b. 0 c. 0 d. 9 Helping You Remember. If ou are going to solve a sstem b elimination, how do ou decide whether ou will need to multipl one or both equations b a number? Lesson - Glencoe/McGraw-Hill Glencoe Algebra
- NAME DATE PERID Enrichment George Washington Carver and Perc Julian In 990, George Washington Carver and Perc Julian became the first African Americans elected to the National Inventors Hall of Fame. Carver ( 9) was an agricultural scientist known worldwide for developing hundreds of uses for the peanut and the sweet potato. His work revitalized the econom of the southern United States because it was no longer dependent solel upon cotton. Julian (9 9) was a research chemist who became famous for inventing a method of making a snthetic cortisone from sobeans. His discover has had man medical applications, particularl in the treatment of arthritis. There are dozens of other African American inventors whose accomplishments are not as well known. Their inventions range from common household items like the ironing board to comple devices that have revolutionized manufacturing. The eercises that follow will help ou identif just a few of these inventors and their inventions. Match the inventors with their inventions b matching each sstem with its solution. (Not all the solutions will be used.). Sara Boone A. (, ) automatic traffic signal 0. Sarah Goode B. (, ) eggbeater 9. Frederick M. C. (, ) fire etinguisher Jones. J. L. Love D. (, ) folding cabinet bed. T. J. Marshall 9 E. (, ) ironing board. Jan Matzeliger F. (, ) pencil sharpener. Garrett A. G. (, 0) portable X-ra machine Morgan. Norbert Rillieu H. (, ) plaer piano I. no solution evaporating pan for refining sugar J. infinitel lasting (shaping) man machine for solutions manufacturing shoes Glencoe/McGraw-Hill Glencoe Algebra
- NAME DATE PERID Stud Guide and Intervention Graphing Sstems of Inequalities Sstems of Inequalities The solution of a sstem of inequalities is the set of all ordered pairs that satisf both inequalities. If ou graph the inequalities in the same coordinate plane, the solution is the region where the graphs overlap. Eample Solve the sstem of inequalities b graphing. The solution includes the ordered pairs in the intersection of the graphs. This region is shaded at the right. The graphs of and are boundaries of this region. The graph of is dashed and is not included in the graph of. Eample Solve the sstem of inequalities b graphing. The graphs of and are parallel. Because the two regions have no points in common, the sstem of inequalities has no solution. Eercises Solve each sstem of inequalities b graphing.... 0 0... Lesson - Glencoe/McGraw-Hill Glencoe Algebra
- Real-World Problems In real-world problems, sometimes onl whole numbers make sense for the solution, and often onl positive values of and make sense. Eample BUSINESS AAA Gem Compan produces necklaces and bracelets. In a 0-hour week, the compan has 00 gems to use. A necklace requires 0 gems and a bracelet requires 0 gems. It takes hours to produce a necklace and a bracelet requires one hour. How man of each tpe can be produced in a week? Let n the number of necklaces that will be produced and b the number of bracelets that will be produced. Neither n or b can be a negative number, so the following sstem of inequalities represents the conditions of the problems. n 0 b 0 b n 0 0b 0n 00 NAME DATE PERID Stud Guide and Intervention (continued) Graphing Sstems of Inequalities The solution is the set ordered pairs in the intersection of the graphs. This region is shaded at the right. nl whole-number solutions, such as (, 0) make sense in this problem. Bracelets 0 0 0 0 0 0 0b 0n 00 b n 0 0 0 0 0 0 Necklaces Eercises For each eercise, graph the solution set. List three possible solutions to the problem.. HEALTH Mr. Flowers is on a restricted. RECREATIN Maria had $0 in gift diet that allows him to have between certificates to use at a record store. She 00 and 000 Calories per da. His bought fewer than 0 recordings. Each dail fat intake is restricted to between tape cost $.9 and each CD cost $.9. and grams. What dail Calorie How man of each tpe of recording might and fat intakes are acceptable? she have bought? 0 0 Fat Grams 0 0 0 0 0 Compact Discs 0 0 t c 0.9t.9c 0 0 000 000 000 Calories 0 0 0 0 Tapes Glencoe/McGraw-Hill Glencoe Algebra
- NAME DATE PERID Skills Practice Graphing Sstems of Inequalities Solve each sstem of inequalities b graphing......... 9. Write a sstem of inequalities for each graph. 0... Lesson - Glencoe/McGraw-Hill 9 Glencoe Algebra
- NAME DATE PERID Practice Graphing Sstems of Inequalities Solve each sstem of inequalities b graphing....... FITNESS For Eercises and, use the following information. Diego started an eercise program in which each week he works out at the gm between. and hours and walks between 9 and miles.. Make a graph to show the number of hours Diego works out at the gm and the number of miles he walks per week.. List three possible combinations of working out and walking that meet Diego s goals. Waking (miles) 0 0 Diego s Routine Gm (hours) SUVENIRS For Eercises 9 and 0, use the following information. Emil wants to bu turquoise stones on her trip to New Meico to give to at least of her friends. The gift shop sells stones for either $ or $ per stone. Emil has no more than $0 to spend. 9. Make a graph showing the numbers of each price of stone Emil can purchase. 0. List three possible solutions. Glencoe/McGraw-Hill 0 Glencoe Algebra
- NAME DATE PERID Reading to Learn Mathematics Graphing Sstems of Inequalities Pre-Activit How can ou use a sstem of inequalities to plan a sensible diet? Read the introduction to Lesson - at the top of page 9 in our tetbook. The green section on the graph represents a range of Calories a da and grams of fat per da. Reading the Lesson Write the inequalit smbols that ou need to get a sstem whose graph looks like the one shown. Use,,, or..... Helping You Remember. Describe how ou would eplain the process of using a graph to solve a sstem of inequalities to a friend who missed Lesson -. Lesson - Glencoe/McGraw-Hill Glencoe Algebra
- NAME DATE PERID Enrichment Describing Regions The shaded region inside the triangle can be described with a sstem of three inequalities. 9 Write sstems of inequalities to describe each region. You ma first need to divide a region into triangles or quadrilaterals.... Glencoe/McGraw-Hill Glencoe Algebra
NAME DATE PERID Chapter Test, Form SCRE Write the letter for the correct answer in the blank at the right of each question. Use the graph for Questions.. The ordered pair (, ) is the solution of which sstem of equations? A. B. C. D.. For Questions, find how man solutions eist for each sstem of equations. A. no solution B. one solution C. infinitel man solutions D. cannot be determined.... 0. When solving the sstem of equations, r s which epression could be substituted r s for r in the second equation? A. s B. r C. s D.. s 0.. Assessment. If and, what is the value of? A. 0 B. C. D. 0.. Use substitution to solve the sstem n m of equations. m n 0 A. (, ) B. (, ) C. (, ) D. (, ).. Use elimination to solve the sstem of equations. A. (, ) B. (, ) C. (, ) D. (, ). 9. Use elimination to solve the sstem 0 of equations. 9 A. (, ) B. (, ) C. (, ) D. (, ) 9. 0. Use elimination to find the value of in 0 the solution for the sstem of equations. A. B. 0 C. D. 0.. To eliminate the variable in the sstem of equations, multipl the second equation b which number? A. B. 9 C. D... Use elimination to solve the sstem of equations. A. ( 9, ) B. (, 9) C. (, ) D. (, ). Glencoe/McGraw-Hill Glencoe Algebra
NAME DATE PERID Chapter Test, Form (continued) For Questions and, determine the best method to solve the sstem of equations. A. substitution B. elimination using addition C. elimination using subtraction D. elimination using multiplication.... Determine which ordered pair represents. a solution of the sstem of inequalities graphed at the right. A. (, ) B. (, ) C. (, ) D. (, ).. Which sstem of inequalities is represented b the graph at the right? A. 0 B. 0 C. 0 D. 0.. An airport shuttle compan owns sedans that have a maimum capacit of passengers and vans that have a maimum capacit of passengers. Their vehicles have a combined maimum capacit of passengers. How man vans does the compan own? A. B. C. D... Find the two numbers whose sum is and whose difference is. A. and B. 9 and C. and D. and 9. 9. Yanc wrote two novels that together contain 0 pages. His longer novel has 0 pages more than his shorter novel. How man pages are contained in Yanc s shorter novel? A. 90 B. 0 C. 0 D. 0 9. 0. The Fotail To Compan makes to cars and to dump trucks. The are scaled so that the door handles and wheels are interchangeable. The table gives the door handle and wheel requirements of each tpe of to. Which sstem of inequalities represents the given information? Wheels Door Handles Parts per To Car Parts per To Dump truck Total Available Parts per da A. B. C. 0 D. 0. Bonus Determine the best method to solve 0 B: the sstem of equations. Then solve 0 the sstem. Glencoe/McGraw-Hill Glencoe Algebra
NAME DATE PERID Chapter Test, Form A SCRE Write the letter for the correct answer in the blank at the right of each question. Use the graph for Questions. For Questions and, determine how man solutions eist for each sstem of equations. A. no solution B. one solution C. infinitel man solutions D. cannot be determined 0... 0.. The solution to which sstem of equations has an value larger than? A. B. C. D. 0. 0. The solution to which sstem of equations has a positive value? A. B. C. D. 0. 0. When solving the sstem of equations, which epression could be substituted for in the second equation? A. B. C. D.. Assessment. If and 9, what is the value of? A. B. C. D... Use elimination to solve the sstem and for. A. B. C. D... Use elimination to solve the sstem 0 and for. A. B. C. 0 D. 0. 9. Use elimination to solve the sstem and 9 for. A. B. C. D. 9. 0. Use elimination to solve the sstem 0 and for. A. B. C. D. 0.. The substitution method should be used to solve which sstem of equations? A. B. C. D... The elimination method using multiplication should be used to solve which sstem of equations? A. B. C. D.. 9 0 Glencoe/McGraw-Hill Glencoe Algebra
NAME DATE PERID Chapter Test, Form A (continued). State which region in the graph is the solution of the sstem. A B C A. A B. B C. C D. D.. Which sstem of inequalities is represented b the graph? A. B. C. D.. For Questions and, solve the sstem and find values of.. A. B. C. D.. 0. 0 A. B. C. D... Two times one number added to three times a second number is. Five times the first number added to three times the second number is 0. What are the numbers? A. and 0 B. and C. and D. and.. Coffee Cafe makes 90 pounds of coffee that costs $ per pound. The tpes of coffee used to make this miture cost $ per pound and $ per pound. How man pounds of the $-per-pound coffee should be used in this miture? A. 0 lb B. 0 lb C. 0 lb D. 0 lb. 9. In 999, there were 9,9 phsicians specializing in Pediatrics in the United States and its possessions. The number of male phsicians minus the number of female phsicians in this categor is. How man female phsicians were there that specialized in Pediatrics in the United States? A. 9, B.,99 C.,00 D., 9. 0. Laurie and Maa make get well cards and friendship cards. The have enough materials to make 0 cards. Laurie and Maa will make at least friendship cards. The also want to make more than 0 get well cards. Which sstem of inequalities represents this information? A. 0 g B. 0 f 0 C. 0 g 0 D. g f 0 0. f 0 g 0 f 0 f g 0 Bonus Where on the graph of is the -coordinate B: twice the -coordinate? Glencoe/McGraw-Hill Glencoe Algebra D
NAME DATE PERID Chapter Test, Form B SCRE Write the letter for the correct answer in the blank at the right of each question. Use the graph for Questions. For Questions and, determine how man solutions eist for each sstem of equations. A. no solution B. one solution C. infinitel man solutions D. cannot be determined.. 0... The solution to which sstem of equations has a positive value? A. 0 B. C. 0 D.. 0. The solution to which sstem of equations has a value less than? A. 0 B. C. 0 D.. 0. When solving the sstem of equations, which epression could be substituted for in the second equation? A. B. C. D.. 0 Assessment. If and, what is the value of? A. B. C. D... Use elimination to solve the sstem and for. A. B. C. D... Use elimination to solve the sstem and 9 for. A. B. C. D.. 9. Use elimination to solve the sstem and for. A. B. C. D. 9. 0. Use elimination to solve the sstem 0 and for. A. B. C. 0 D. 0.. The substitution method should be used to solve which sstem of equations? A. B. C. D... The elimination method using addition should be used to solve which sstem of equations? A. B. C. D. 9. Glencoe/McGraw-Hill Glencoe Algebra
NAME DATE PERID Chapter Test, Form B (continued). State which region in the graph is the solution of the sstem. A. A B. B D C. C D. D.. Which sstem of inequalities is represented b the graph? A. B. C. D.. For Questions and, solve the sstem and find the value of.. A. B. C. D.. 9. A. 0 B. C. 0 D. 9. 0. Five times one number minus two times a second number is. Three times the first number minus two times the second number is. What are the numbers? A. and B. and C. and D. and.. Colortime Bakers wants to make 0 pounds of a berr mi that costs $ per pound to use in their pancake mi. The are using blueberries that cost $ per pound and blackberries that cost $.0 per pound. How man pounds of blackberries should be used in this miture? A. lb B. 0 lb C. 0 lb D. 0 lb. 9. In 999, there were 9,0 phsicians specializing in Famil Practice in the United States and its possessions. The number of male phsicians minus the number of female phsicians in this categor is,9. How man female phsicians were there that specialized in Famil Practice in the United States? A. 0, B., C. D., 9. 0. Beng and Shim make boat-shaped candles and dog-shaped candles. The have enough materials to make 0 candles. Beng and Shim will make at most 0 boat-shaped candles. The will also make less than dog-shaped candles. Which sstem of inequalities represents this information? A. b 0 B. 0 d 0 C. b d 0 D. 0 b 0 0. 0 d b 0 0 b 0 0 d 0 d Bonus Manuel is ears older than his sister. Three ears ago B: he was times older than his sister. How old is each now? A B C Glencoe/McGraw-Hill Glencoe Algebra
NAME DATE PERID Chapter Test, Form C SCRE Use the graph at the right to determine whether each sstem has no solution, one solution, or infinitel man solutions.. 0... Assessment. Graph each sstem of equations. Then determine whether the sstem has no solution, one solution, or infinitel man solutions. If the sstem has one solution, name it.... 9.. Use substitution to solve each sstem of equations. If the sstem does not have eactl one solution, state whether it has no solution or infinitel man solutions... 0. 9. 0 0 0. Use elimination to solve each sstem of equations. 0.... 9... 9 0.... 0.. Determine the best method to solve each sstem of equations. Then solve the sstem....... Glencoe/McGraw-Hill 9 Glencoe Algebra
NAME DATE PERID Chapter Test, Form C (continued) For Questions and 9, solve each sstem of inequalities b graphing... 9. 9. 0. The sum of two numbers is and their difference is 9. What are the two numbers?. Adult tickets for the school musical sold for $.0 and student tickets sold for $.0. Three hundred twent-one tickets were sold altogether for $9.0. How man of each kind of ticket were sold? 0.. Aana has $. in nickels and dimes. If she has coins in all, find the number of nickels and dimes... The largest count in the state of New York is 9 square miles larger than the smallest count in the same state. The size of the largest count is times the size of the smallest count plus five square miles. How large is the smallest count in the state of New York?.. For Questions and, use the following information.. The Martinez Compan manufactures two tpes of industrial fans, standard and econom. These items are built using machines and manual labor. The table gives the time requirements at each tpe of workstation for each tpe of fan. e 00 00 00 Hours per Standard Fan Hours per Econom Fan Total Available Hours Each Week Machines 00 00 00 00 00 00 s Manual Labor 00. Make a graph showing the number of standard fans and the number of econom fans that can be made in a week.. List three possible solutions.. Bonus Mavis is ears older than her brother. Five ears ago B: she was times older than her brother. How old is each now? Glencoe/McGraw-Hill 0 Glencoe Algebra
NAME DATE PERID Chapter Test, Form D SCRE Use the graph at the right to determine whether each sstem has no solution, one solution, or infinitel man solutions...... Assessment Graph each sstem of equations. Then determine whether the sstem has no solution, one solution, or infinitel man solutions. If the sstem has one solution, name it.... 0. 0. Use substitution to solve each sstem of equations. If the sstem does not have eactl one solution, state whether it has no solution or infinitel man solutions.... 9. 0 Use elimination to solve each sstem of equations. 0. 9. 0... 9... 9 0.... 0.. Determine the best method to solve each sstem of equations. Then solve the sstem... 0 9.... Glencoe/McGraw-Hill Glencoe Algebra
NAME DATE PERID Chapter Test, Form D (continued) For Questions and 9, solve each sstem of inequalities b graphing... 9. 9. 0. The sum of two numbers is and their difference is 0. What are the two numbers?. Kle just started a new job that pas $ per hour. He had been making $ per hour at his old job. Kle worked a total of hours last month and made $ before deductions. How man hours did he work at his new job?. So far this basketball season, all of Nikki s points have come from two-point and three-point field goals. She has scored a total of points. The number of three-point field goals she has made is one more than twice as man two-point field goals. How man of each tpe of field goal has Nikki made? 0.... The largest count in the state of Teas is 0 square miles larger than the smallest count in the same state. The size of the largest count is times the size of the smallest count plus one square mile. How large is the smallest count in the state of Teas?. For Questions and, use the following information.. The Tadashi Corporation manufactures a large speaker and a small speaker for phone headsets. The speakers are used on the Tadashi 00 and the Tadashi 00 phone sstems. The table gives the speaker requirement for each phone sstem. 00 00 00 Speakers on Tadashi 00 Speakers on Tadashi 00 Total Available Speakers Each Week Large Speaker 900 00 00 00 00 00 Small Speaker 000. Make a graph showing the number of Tadashi 00 and Tadashi 00 phone sstems that can be made in a week.. List three possible solutions.. Bonus Find the point on the graph of 9 where the B: -coordinate is times the -coordinate. Glencoe/McGraw-Hill Glencoe Algebra
NAME DATE PERID Chapter Test, Form SCRE Determine whether each sstem has no solution, one solution, or infinitel man solutions b graphing each sstem... Graph each sstem of equations. Determine whether the sstem has no solution, one solution, or infinitel man solutions. If the sstem has one solution, name it.... Assessment. 0. 9. 0. Use substitution to solve each sstem of equations. If the sstem does not have eactl one solution, state whether it has no solution or infinitel man solutions..... 9 9. 0.. 0 Use elimination to solve each sstem of equations. 0.. 0. 0. 0. 0. 0....... 0 9. 0... 0. 0.. 0. 0..... Determine the best method to solve each sstem of equations. Then solve the sstem..... 0. Glencoe/McGraw-Hill Glencoe Algebra
NAME DATE PERID Chapter Test, Form (continued) For Questions and 9, solve each sstem of inequalities b graphing... 9. 9. 0. Three times one number added to five times a second number is. Three times the second number minus four times the first number is. What are the two numbers?. The difference of two numbers is. Five times the lesser number minus the greater number is 9. What are the two numbers?. The sum of the digits of a -digit number is. If the digits are reversed, the new number is 9 more than the original number. Find the original number.. A trail mi that costs $. per pound is mied with a trail mi that costs $.0 per pound. How much of each tpe of trail mi must be used to have 0 pounds of a trail mi that costs $. per pound? 0....... A boat travels 0 miles downstream in the same time it takes to go miles upstream. The speed of the boat in still water is mph greater than the speed of the current. Find the speed of the current.. Mrs. Lewis needs to bu two tpes of grain, oats and barle, to mi as a feed supplement for her cattle. She has $,000 to spend on grain, and wants the miture to be at most parts oats per parts barle. She can bu oats for $.0 per bushel and barle for $.0 per bushel. If Mrs. Lewis needs at least 00 bushels of grain, make a graph showing the number of bushels of oats and the number of bushels of barle that she should bu, and list three possible solutions. Bonus Graph the solution set of. B: Glencoe/McGraw-Hill Glencoe Algebra
NAME DATE PERID Chapter pen-ended Assessment SCRE Demonstrate our knowledge b giving a clear, concise solution to each problem. Be sure to include all relevant drawings and justif our answers. You ma show our solution in more than one wa or investigate beond the requirements of the problem.. Ruth invests $0,000 in two accounts. ne account has an annual interest rate of %, and the other account has an annual interest rate of %. Let I represent the total interest earned in one ear. Then Ruth s investments can be modeled b the sstem of equations 0,000 and 0.0 0.0 I. a. Determine a solution for this sstem of equations that represents a possible investment, and find the value of I that corresponds to our solution. b. Find the solution for the sstem if I 00. Eplain wh this solution does not represent a possible investment.. A car rental compan wants to charge a rate of $A per da plus $B per mile to rent a compact car. Their leading competitor charges $ per da plus $0. per mile to rent a compact car. a. Eplain how the sstem of equations A B and 0. compares the total cost of renting a compact car for one da from this compan and from their leading competitor. b. Describe how the value of A and the value of B affects the comparison of the total cost of an one-da rental from these two companies. Assessment. A bookstore makes a profit of $.0 on each book the sell, and $0. on each magazine the sell. Each week the store sells books and magazines. Let $P be the weekl profit, and $S be the weekl sales for the bookstore. a. Write a sstem of equations that models the possible weekl sales and weekl profit for the book store. Then describe possible values for P and S. b. Replace the equal signs in the sstem of equations from part a with inequalit smbols to create a sstem of inequalities. Eplain how these two sstems differ in modeling the weekl profit and weekl sales of the bookstore. Eplain how these two sstems are the same. c. Choose a value for P and a value for S, and substitute the values into the sstem of inequalities from part b. Make a graph of this sstem of inequalities, and describe what the graph represents. Glencoe/McGraw-Hill Glencoe Algebra
NAME DATE PERID Chapter Vocabular Test/Review SCRE consistent dependent elimination inconsistent independent substitution sstem of equations sstem of inequalities Underline or circle the correct term to complete each sentence.. Two equations, such as and, together are called a?. sstem of inequalities sstem of equations solution of a sstem. If the graphs of the equations of a sstem intersect or coincide, the sstem of equations is?. consistent inconsistent independent. If the graphs of the equations of a sstem are parallel, the sstem is?. consistent inconsistent dependent. If a sstem of equations has eactl one solution, the sstem is?. inconsistent dependent independent. If a sstem of equations has an infinite number of solutions, the sstem is?. inconsistent dependent independent. Sometimes adding two equations of a sstem will give an equation with onl one variable. This is helpful when ou are solving the sstem b?. graphing substitution elimination. For a sstem where one variable is solved in terms of the other variable, ou can solve the sstem b using?. addition substitution elimination In our own words Define the term.. sstem of inequalities Glencoe/McGraw-Hill Glencoe Algebra
NAME DATE PERID Chapter Quiz (Lessons and ) SCRE Graph each sstem of equations. Then determine whether the sstem has no solution, one solution, or infinitel man solutions. If the sstem has one solution, name it... Assessment.. For Questions and, use substitution to solve each sstem of equations. If the sstem does not have eactl one solution, state whether it has no solutions or infinitel man solutions.... 0. 0. In order for José and Mart to compete against each other. during the wrestling season net ear the need to be in the same weight categor. José weighs 0 pounds and plans to gain pounds per week. Mart weighs 0 pounds and plans to lose pound per week. In which week will the weigh the same? NAME DATE PERID Chapter Quiz (Lesson ) SCRE For Questions, use elimination to solve each sstem of equations....... r s. r s 9 0.. Standardized Test Practice If and, what is the value of? A. B. C. D.. Glencoe/McGraw-Hill Glencoe Algebra
NAME DATE PERID Chapter Quiz (Lesson ) SCRE Use elimination to solve each sstem of equations... 0. r s 9. r s. c d 0. c d Determine the best method to solve each sstem of. equations. Then solve the sstem... 9. NAME DATE PERID Chapter Quiz (Lesson ) SCRE For Questions, solve each sstem of inequalities b. graphing..... Adult tickets to the school musical are $ and. student tickets are $. There are 00 seats in the auditorium where the musical is being performed. The goal for ticket sales for one performance is at least $900. Make a graph showing the number of each kind of ticket needed to be sold to reach the goal. List three possible solutions. s 00 00 00 00 00 00 00 00 a Glencoe/McGraw-Hill Glencoe Algebra
NAME DATE PERID Chapter Mid-Chapter Test (Lessons through ) SCRE Part I Write the letter for the correct answer in the blank at the right of each question. Use the graph for Questions. For Questions and, determine how man solutions eist for each sstem of equations. A. no solution B. one solution C. infinitel man solutions D. cannot be determined.... Assessment. The solution to which sstem of equations has a positive value? A. B. C. D... If and, what is the value of? A. B. C. D... Use elimination to solve the sstem of equations for. A. B. C. D... How man solutions does the sstem 0 and have? Part II A. one B. two C. none D. infinitel man.. Graph the sstem of equations. Then determine whether it has no solution, one solution, or infinitel man solutions. If the sstem has one solution name it. 9. Use substitution to solve the 0 sstem of equations. For Questions 9, use elimination to solve each sstem of equations. 9. 0. 0.. 9.. 9. At the end of the 000 WNBA regular season, the Houston Comets had more victories than losses. The number of victories the had was three less than si times the number of losses. How man regular season games did the Houston Comets pla during the 000 WNBA season? 0... Glencoe/McGraw-Hill 9 Glencoe Algebra
NAME DATE PERID Chapter Cumulative Review (Chapters ). Solve a. (Lesson -).. Find the coordinates of the vertices of triangle DEF with. D(, ), E(, ), and F(, ) rotated 90 clockwise about the origin. (Lesson -). Solve if the domain is {,, 0,, }. (Lesson -).. Write the slope-intercept form of an equation of the line. that passes through (0, ) and is parallel to the graph of. (Lesson -). Solve a. (Lesson -).. Write an open sentence. involving absolute value for the graph. (Lesson -) 0. Graph the sstem of equations. Then determine whether. the sstem has no solution, one solution, or infinitel man solutions. (Lesson -). Jim s Brakes charges $ for parts and $ per hour to fi. the brakes on a car. Mron s Auto charges $0 for parts and $0 per hour to do the same job. What length of job in hours would have the same cost at both shops? (Lesson -) 9. The sum of two numbers is, and their difference is. 9. What are the numbers? (Lesson -) 0. Use elimination to solve the sstem of equations. (Lesson -) 0.. Solve the sstem of inequalities b graphing. (Lesson -). Glencoe/McGraw-Hill 0 Glencoe Algebra
NAME DATE PERID Standardized Test Practice (Chapters ) Part : Multiple Choice Instructions: Fill in the appropriate oval for the best answer.. Which equation is not equivalent to? (Lesson -) A. 9 B. 0 9 C. 9 D... Find the value of so that the line through (, ) and (, ) has a slope of. (Lesson -) A B C D Assessment E. F. G. 9 H. 9. E F G H. Solve r 0. (Lesson -) 9 A. r r 9 B. r r 9 C. r r D. r r. A B C D. Write a compound inequalit for the graph. (Lesson -) 0 E. or F. and G. H.. E F G H. Which inequalit is represented b a dashed line through (0, ) and (, 0), and is satisfied b (, )? (Lesson -) A. B. C. D.. A B C D. How man solutions eist for the sstem of equations? (Lesson -) E. no solutions F. one solution G. two solutions H. infinitel man solutions. E F G H. When solving the following sstem, which epression could be substituted for? (Lesson -) A. B. C. D.. A B C D. If and, what is the value of? (Lesson -) E. F. G. H.. E F G H 9. Which ordered pair satisfies the sstem of inequalities? (Lesson -) 0 A. (0, ) B. (, ) C. (, ) D. (, ) 9. A B C D Glencoe/McGraw-Hill Glencoe Algebra
NAME DATE PERID Standardized Test Practice (continued) Part : Grid In Instructions: Enter our answer b writing each digit of the answer in a column bo and then shading in the appropriate oval that corresponds to that entr. 0. Find ( ). (Lesson -) 0.. 9. If f(), find f( ). (Lesson -) / /... 0 0 0. 9 9 9 9 / /... 0 0 0. 9 9 9 9. What is the slope of a line parallel to the.. line that passes through (, ) and (, )? (Lesson -). If and, what is the value of? (Lesson -) / /... 0 0 0. 9 9 9 9 / /... 0 0 0 9 9 9 9. Part : Quantitative Comparison Instructions: Compare the quantities in columns A and B. Shade in A if the quantit in column A is greater; B if the quantit in column B is greater; C if the quantities are equal; or D if the relationship cannot be determined from the information given. Column A Column B. 9. A B C D (Lesson -). Given: parallelogram ABCD with A(, ), B(, ), C(, ), and. D(, ) rotated 90 counterclockwise about the origin. (Lesson -) A B C D the -coordinate of B the -coordinate of D. Given: and. (Lessons - and -). A B C D Glencoe/McGraw-Hill Glencoe Algebra
NAME DATE PERID Unit Test (Chapters ) SCRE. Trapezoid WXYZ with W(, ), X(, ), Y(, ), and. Z(, ) is translated units right. Find the coordinates of the vertices of the figure after the transformation is performed. Then graph the preimage and its image. Assessment. Epress the relation shown in the. mapping as a set of ordered pairs. Then write the inverse of the relation.. Solve if the domain is {,, 0,, }... Graph.. X Y. If g(), find g( )... Find the th term of the arithmetic sequence with first. term and common difference.. Find the net three terms in the sequence,,,,... A giraffe can travel 00 feet in 0 seconds. Write a direct. variation equation for the distance traveled in an time. 9. Write an equation of the line whose slope is and whose 9. -intercept is 9. 0. Write an equation of the line that passes through (, ) 0. and (, ).. Write ( ) in standard form... Write the slope-intercept form of an equation of the line. that passes through (, 0) and is parallel to the graph of. Glencoe/McGraw-Hill Glencoe Algebra
NAME DATE PERID Unit Test (continued). The table below shows the distance driven during four. different trips and the duration of each trip. Draw a scatter plot and determine what relationship eists, if an, in the data. Write an equation for a line of fit for the data. Time (hours). Distance (miles) 0 0 0 Distance (miles) 0 0 0 0 0 Time (hours) Solve each inequalit.. 0.. (a ) ( a). Solve each compound inequalit.. t.. v or v. For Questions and 9, solve each open sentence. Then graph the solution set.. b. 0 9. w 9. 0 0. Use a graph to determine whether the sstem 0. and has no solution, one solution, or infinitel man solutions. For Questions, determine the best method to solve each sstem of equations. Then solve the sstem.......... Solve the sstem of inequalities b graphing.. Glencoe/McGraw-Hill Glencoe Algebra
NAME DATE PERID Standardized Test Practice Student Record Sheet (Use with pages 0 0 of the Student Edition.) Part Multiple Choice Select the best answer from the choices given and fill in the corresponding oval. A B C D A B C D A B C D 9 A B C D A B C D A B C D A B C D 0 A B C D A B C D A B C D Part Short Response/Grid In Solve the problem and write our answer in the blank. Answers For Questions, also enter our answer b writing each number or smbol in a bo. Then fill in the corresponding oval for that number or smbol. (grid in) (grid in) / /.... / /.... / /.... 0 0 0 0 0 0 0 0 0 (grid in) 9 9 9 9 9 9 9 9 9 9 9 9 Part Etended Response Record our answers for Questions 9 on the back of this paper. Glencoe/McGraw-Hill A Glencoe Algebra