ALGEBRA 1 UNIT 3 WORKBOOK CHAPTER 6
|
|
- Ethelbert Manning
- 5 years ago
- Views:
Transcription
1 ALGEBRA 1 UNIT 3 WORKBOOK CHAPTER 6 FALL
2 1
3 Algebra 1 Section 6.1 Notes: Graphing Systems of Equations System of Equations: a set of two or more equations with the same variables, graphed in the same coordinate plane The ordered pair that is a solution of both equations is the solution of the system. A system of two linear equations can have one solution, an infinite number of solutions, or no solution. Consistent: a system of equations that has at least one solution Independent: a consistent system of equations that has exactly one solution Dependent: a consistent system of equations that has an infinite number of solutions; this means that there are an unlimited solutions that satisfy both equations Inconsistent: a system of equations that has no solution; the graphs are parallel Example 1: Use the graph to determine whether the system is consistent or inconsistent and if it is independent or dependent. a) y = x + 1 b) y = x 3 y = x + 4 y = x + 1 Solve by Graphing: One method of solving a system of equations is to graph the equations on the same coordinate plane and find their point of intersection. This point is the solution of the system. Example 2: Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it. a) y = 2x + 3 8x 4y = 12 2
4 b) x 2y = 4 c) x y = 2 x 2y = 2 3y + 2x = 9 We can use what we know about systems of equations to solve many real-world problems involving constraints that are modeled by two or more different functions. Example 3: Naresh and Diego are having a bicycling competition. Naresh is able to ride 20 miles at the start of the competition and plans to ride 35 more miles than the previous week each upcoming week. Diego is able to ride 50 miles at the start of the competition and plans to ride 25 more miles than the previous week each upcoming week. Predict the week in which Naresh and Diego will have ridden the same number of miles. 1) Write a system of equations to represent the system 2) Graph the system to determine the solution. 3) Use substitution to check your answer. Example 4: Alex and Amber are both saving money for a summer vacation. Alex has already saved $100 and plans to save $25 per week until the trip. Amber has $75 and plans to save $30 per week. In how many weeks will Alex and Amber have the same amount of money? 3
5 Algebra 1 Section 6.1 Worksheet Use the graph at the right to determine whether each system is consistent or inconsistent and if it is independent or dependent. 1. x + y = x y = 3 x + y = 3 4x 2y = 6 3. x + 3y = 3 4. x + 3y = 3 x + y = 3 2x y = 3 Graph each system and determine the number of solutions that it has. If it has one solution, name it. 5. 3x y = 2 6. y = 2x 3 7. x + 2y = 3 3x y = 0 4x = 2y + 6 3x y = 5 8. BUSINESS Nick plans to start a home-based business producing and selling gourmet dog treats. He figures it will cost $20 in operating costs per week plus $0.50 to produce each treat. He plans to sell each treat for $1.50. a. Graph the system of equations y = 0.5x + 20 and y = 1.5x to represent the situation. b. How many treats does Nick need to sell per week to break even? 9. SALES A used book store also started selling used CDs and videos. In the first week, the store sold 40 used CDs and videos, at $4.00 per CD and $6.00 per video. The sales for both CDs and videos totaled $ a. Write a system of equations to represent the situation. b. Graph the system of equations. c. How many CDs and videos did the store sell in the first week? 4
6 Algebra 1 Section 6.2 Notes: Substitution In the previous lesson, we learned how to solve a system of equations by graphing. Another method for solving a system of equation is called substitution. Example 1: Use substitution to solve the system of equations. a) y = 4x + 12 b) y = 4x 6 2x + y = 2 5x + 3y = -1 If a variable is not isolated in one of the equations in the system, solve an equation for a variable first. Then you can use substitution so solve the system. Example 2: Use substitution to solve the system of equations. a) x 2y = 3 b) 3x y = 12 3x + 5y = 24 4x + 2y = 20 5
7 Generally, if you solve a system of equations and the result is a false statement such as 3 = -2, there is no solution. If the result is an identity, such as 3 = 3, then there are an infinite number of solutions. Example 3: Use substitution to solve the system of equations. a) 2x + 2y = 8 b) 3x 2y = 3 x + y = 2 6x + 4y = 6 Example 4: a) A nature center charges $35.25 for a yearly membership and $6.25 for a single admission. Last week it sold a combined total of 50 yearly memberships and single admissions for $ How many memberships and how many single admissions were sold? b) As of 2009, the New York Yankees and the Cincinnati Reds together had won a total of 32 World Series. The Yankees had won 5.4 times as many as the Reds. How many World Series had each team won? 6
8 Algebra Worksheet Use substitution to solve each system of equations. 1. y = 6x 2. x = 3y 3. x = 2y + 7 2x + 3y = 20 3x 5y = 12 x = y y = 2x 2 5. y = 2x x + y = 12 y = x + 2 2x y = 2 y = x 2 7. x + 2y = x 2y = 3 9. x 5y = 36 2x 3y = 18 4x 8y = 12 2x + y = x 3y = x + 14y = x 0.2y = 0.5 x + 6y = 18 2x 7y = 7 x 2y = x + 4y = x 2y = x + 2y = 12 2 x + 2.5y = 3.5 x 1 y = 4 2 x 2y = x y = x 5y = x + 3y = 4 2x + y = 25 y = 5x 2x + 6y = 5 7
9 19. EMPLOYMENT Kenisha sells athletic shoes part-time at a department store. She can earn either $500 per month plus a 4% commission on her total sales, or $400 per month plus a 5% commission on total sales. a. Write a system of equations to represent the situation. b. What is the total price of the athletic shoes Kenisha needs to sell to earn the same income from each pay scale? c. Which is the better offer? 20. MOVIE TICKETS Tickets to a movie cost $7.25 for adults and $5.50 for students. A group of friends purchased 8 tickets for $ a. Write a system of equations to represent the situation. b. How many adult tickets and student tickets were purchased? 21. BUSINESS Mr. Randolph finds that the supply and demand for gasoline at his station are generally given by the following equations. x y = 2 x + y = 10 Use substitution to find the equilibrium point where the supply and demand lines intersect. 22. GEOMETRY The measures of complementary angles have a sum of 90 degrees. Angle A and angle B are complementary, and their measures have a difference of 20. What are the measures of the angles? 23. MONEY Harvey has some $1 bills and some $5 bills. In all, he has 6 bills worth $22. Let x be the number of $1 bills and let y be the number of $5 bills. Write a system of equations to represent the information and use substitution to determine how many bills of each denomination Harvey has. 24. POPULATION Sanjay is researching population trends in South America. He found that the population of Ecuador to increased by 1,000,000 and the population of Chile to increased by 600,000 from 2004 to The table displays the information he found. Country 2004 Population 5-Year Population Change Ecuador 13,000,000 +1,000,000 Chile 16,000, ,000 Source: World Almanac If the population growth for each country continues at the same rate, in what year are the populations of Ecuador and Chile predicted to be equal? 8
10 Algebra 1 Section 6.3 Notes: Elimination Using Addition and Subtraction You have learned about solving a system of equations using the graphing method and the substitution method. A third way to solve a system of equations is called elimination. Elimination involves using addition or subtraction to solve a system. Example 1: Use elimination to solve the system of equations. a) 3x + 4y = 12 b) 3x 5y = 1 3x 6y = 18 2x + 5y = 9 Example 2: Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Write a system of linear equations and then use elimination to solve it and find the numbers. Example 3: Use elimination to solve the system of equations. a) 4x + 2y = 28 b) 9x 2y = 30 4x 3y = 18 x 2y = 14 9
11 Example 4: a) A hardware store earned $ from renting ladders and power tools last week. The store charged 36 days for ladders and 85 days for power tools. This week the store charged 36 days for ladders, 70 days for power tools, and earned $829. How much does the store charge per day for ladders and for power tools? b) For a school fundraiser, Marcus and Anisa participated in a walk-a-thon. In the morning, Marcus walked 11 miles and Anisa walked 13. Together they raised $ After lunch, Marcus walked 14 miles and Anisa walked 13. In the afternoon they raised $ How much did each raise per mile of the walk-a-thon? 10
12 Algebra Worksheet Use elimination to solve each system of equations. 1. x y = 1 2. p + q = x + y = 23 x + y = 9 p q = 8 3x y = x + 5y = x + 2y = x + 3y = 22 2x + 2y = 6 4x + 2y = 6 5x 2y = x + 2y = x 9y = c 2d = 2 2x + 2y = 14 3x 15y = 6 2c 2d = x 6y = x + 2y = x 1.28y = 9.2 2x + 3y = 24 7x 2y = 30 x y = x + 4y = x + y = m 8n = 3 x 4y = x + 2y = m 8n = a + b = x 4 3 = x 1 2 y = 8 4a + 3b = 10 1 x 2 y = 4 3 x 1 y =
13 19. The sum of two numbers is 41 and their difference is 5. What are the numbers? 20. Four times one number added to another number is 36. Three times the first number minus the other number is 20. Find the numbers. 21. One number added to three times another number is 24. Five times the first number added to three times the other number is 36. Find the numbers. 22. LANGUAGES English is spoken as the first or primary language in 78 more countries than Farsi is spoken as the first language. Together, English and Farsi are spoken as a first language in 130 countries. In how many countries is English spoken as the first language? In how many countries is Farsi spoken as the first language? 23. DISCOUNTS At a sale on winter clothing, Cody bought two pairs of gloves and four hats for $ Tori bought two pairs of gloves and two hats for $ What were the prices for the gloves and hats? 12
14 Algebra 1 Section 6.4 Notes: Elimination Using Multiplication Two systems don t always have to have the same or opposite coefficients for a variable to use elimination. You can use multiplication and elimination to solve a system when this is the case. Example 1: Use elimination to solve the system of equations. a) 2x + y = 23 b) x + 7y = 12 3x + 2y = 37 3x 5y = 10 Example 2: Use elimination to solve the system of equations. a) 4x + 3y = 8 b) 3x + 2y = 10 3x 5y = 23 2x + 5y = 3 13
15 Example 3: a) A fishing boat travels 10 miles downstream in 30 minutes. The return trip takes the boat 40 minutes. Find the rate in miles per hour of the boat in still water. b) A helicopter travels 360 miles with the wind in 3 hours. The return trip against the wind takes the helicopter 4 hours. Find the rate of the helicopter in still air. 14
16 Algebra Worksheet Use elimination to solve each system of equations. 1. 2x y = x 2y = x + 4y = 4 3x 2y = 1 3x + 6y = 66 5x + 8y = x 4y = x + 2y = x 2y = 32 3x + 3y = 30 5x 3y = 4 3x 5y = x + 4y = x + 0.5y = x 3 y = 7 4 5x 3y = 16 x 0.25y = 6 x y = x 3y = x + 2y = x + 2y = 15 2x + 2y = 22 2x + 6y = 2 2x 4y = 26 15
17 13. Eight times a number plus five times another number is 13. The sum of the two numbers is 1. What are the numbers? 14. Two times a number plus three times another number equals 4. Three times the first number plus four times the other number is 7. Find the numbers. 15. FINANCE Gunther invested $10,000 in two mutual funds. One of the funds rose 6% in one year, and the other rose 9% in one year. If Gunther s investment rose a total of $684 in one year, how much did he invest in each mutual fund? 16. CANOEING Laura and Brent paddled a canoe 6 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. 17. NUMBER THEORY The sum of the digits of a two-digit number is 11. If the digits are reversed, the new number is 45 more than the original number. Find the number. 16
18 Algebra 1 Section 6.5 Notes: Applying Systems of Linear Equations You have learned five methods for solving systems of linear equations. The table summarizes the methods and the types of systems for which each method works best. Example 1: a) Determine the best method to solve the system of equations. Then solve the system. 2x + 3y = 23 4x + 2y = 34 b) POOL PARTY At the school pool party, Mr. Lewis bought 1 adult ticket and 2 child tickets for $10. Mrs. Vroom bought 2 adult tickets and 3 child tickets for $17. Write a system of linear equations for this situation and then determine the best method to solve the system of equations. Then solve the system. 17
19 Example 2: a) CAR RENTAL Ace Car Rental rents a car for $45 and $0.25 per mile. Star Car Rental rents a car for $35 and $0.30 per mile. How many miles would a driver need to drive before the cost of renting a car at Ace Car Rental and renting a car at Star Car Rental were the same? b) VIDEO GAMES The cost to rent a video game from Action Video is $2 plus $0.50 per day. The cost to rent a video game at TeeVee Rentals is $1 plus $0.75 per day. After how many days will the cost of renting a video game at Action Video be the same as the cost of renting a video game at TeeVee Rentals? 18
20 Algebra Worksheet Determine the best method to solve each system of equations. Then solve the system. 1. 5x + 3y = x 5y = 7 3x 5y = 4 2x + 5y = y = 3x x 10y = 17 5x y = 8 5x 7y = x + y = x y = 145 5x y = 12 x = 4 2y 19
21 7. VEGETABLE STAND A roadside vegetable stand sells pumpkins for $5 each and squashes for $3 each. One day they sold 6 more squash than pumpkins, and their sales totaled $98. Write and solve a system of equations to find how many pumpkins and quash they sold? 8. INCOME Ramiro earns $20 per hour during the week and $30 per hour for overtime on the weekends. One week Ramiro earned a total of $650. He worked 5 times as many hours during the week as he did on the weekend. Write and solve a system of equations to determine how many hours of overtime Ramiro worked on the weekend. 9. BASKETBALL Anya makes 14 baskets during her game. Some of these baskets were worth 2-points and others were worth 3- points. In total, she scored 30 points. Write and solve a system of equations to find how 2-points baskets she made. 20
22 Algebra 1 Section 6.6 Notes: Systems of Inequalities A set of two or more inequalities with the same variable is called a system of inequalities. The solution of a system of inequalities with two variables is the set of ordered pairs that satisfy all of the inequalities in the system. The solution set is represented by the overlap, or intersection, of the graphs of the inequalities. Example 1: a) Solve the system of inequalities by graphing. y < 2x + 2 y x 3 b) Choose the correct solution to the system: 2x + y 4 and x + 2y > 4. A. B. C. D. 21
23 Example 2: Solve the system of inequalities by graphing. y 3x + 1 y 3x 2 Example 3: a) SERVICE A college service organization requires that its members maintain at least a 3.0 grade point average, and volunteer at least 10 hours a week. Define the variables and write a system of inequalities to represent this situation. Then graph the system. b) SERVICE A college service organization requires that its members maintain at least a 3.0 grade point average, and volunteer at least 10 hours a week. Name one possible solution. \ 22
24 Algebra Worksheet Solve each system of inequalities by graphing. 1. y > x 2 2. y x x + y 1 y x y > 2x + 3 x + 2y > 1 4. y < 2x 1 5. y > x x y 2 y > 2 x 2x + y 2 x 2y 2 7. FITNESS Diego started an exercise program in which each week he works out at the gym between 4.5 and 6 hours and walks between 9 and 12 miles. a. Make a graph to show the number of hours Diego works out at the gym and the number of miles he walks per week. b. List three possible combinations of working out and walking that meet Diego s goals. 8. SOUVENIRS Emily wants to buy turquoise stones on her trip to New Mexico to give to at least 4 of her friends. The gift shop sells stones for either $4 or $6 per stone. Emily has no more than $30 to spend. a. Make a graph showing the numbers of each price of stone Emily can purchase. b. List three possible solutions. 23
ALGEBRA 1. Unit 3 Chapter 6. This book belongs to: Teacher:
ALGEBRA 1 Teacher: Unit 3 Chapter 6 This book belongs to: UPDATED FALL 2016 1 2 Algebra 1 Section 6.1 Notes: Graphing Systems of Equations Day 1 Warm-Up 1. Graph y = 3x 1 on a coordinate plane. 2. Check
More informationChapter 6: Systems of Linear Equations and Inequalities
Lesson 6-1: Graphing Sstems of Equations Date: Eample 1: Use the graph to determine whether each sstem is consistent or inconsistent and if it is independent or dependent. a. = 1 and = + 1 b. = 1 and =
More informationStudy Guide and Intervention
7-3 Study Guide and Intervention Elimination Using Addition and Subtraction Elimination Using Addition In systems of equations in which the coefficients of the x or y terms are additive inverses, solve
More informationYou solved systems of equations by using substitution.
You solved systems of equations by using substitution. LEQ: How do we solve systems of equations by using elimination with addition & solve systems of equations by using elimination with subtraction? elimination
More informationChapter 4: Systems of Equations and Inequalities
Chapter 4: Systems of Equations and Inequalities 4.1 Systems of Equations A system of two linear equations in two variables x and y consist of two equations of the following form: Equation 1: ax + by =
More informationNAME DATE PERIOD. Graphing Equations in Slope-Intercept Form
NAME DATE PERID 4-1 Skills Practice Graphing Equations in Slope-Intercept Form Write an equation of a line in slope-intercept form with the given slope and -intercept. 1. slope: 5, -intercept: -3. slope:
More informationSection 2.2 Objectives
Section 2.2 Objectives Solve multi-step equations using algebra properties of equality. Solve equations that have no solution and equations that have infinitely many solutions. Solve equations with rational
More informationFinal Exam Study Guide
Algebra 2 Alei - Desert Academy 2011-12 Name: Date: Block: Final Exam Study Guide 1. Which of the properties of real numbers is illustrated below? a + b = b + a 2. Convert 6 yards to inches. 3. How long
More informationIntroduction to Systems of Equations
Systems of Equations 1 Introduction to Systems of Equations Remember, we are finding a point of intersection x 2y 5 2x y 4 1. A golfer scored only 4 s and 5 s in a round of 18 holes. His score was 80.
More information3-1 Solving Systems of Equations. Solve each system of equations by using a table. 1. ANSWER: (3, 5) ANSWER: (2, 7)
Solve each system of equations by using a table. 1. 9. CCSS MODELING Refer to the table below. (3, 5) 2. (2, 7) Solve each system of equations by graphing. 3. a. Write equations that represent the cost
More informationThe graphs intersect. Therefore, there is one solution. The. The solution is (3, 1). many solutions.
Answers (Lesson 7-) Lesson 7-7- 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.
More informationName. Check with teacher. equation: a. Can you find. a. (-2, -3) b. (1, 3) c. (2, 5) d. (-2, -6) a. (-2, 6) b. (-1, 1) c. (1, 3) d. (0, 0) Explain why
7.1 Solving Systems of Equations: Graphing Name Part I - Warm Up with ONE EQUATION: a. Which of the following is a solution to the equation: y 3x 1? a. (-2, -3) b. (1, 3) c. (2, 5) d. (-2, -6) Partt II
More informationAdditional Exercises 5.1 Form I
Additional Exercises 5.1 Form I Solving Systems of Linear Equations by Graphing Determine whether the given ordered pair is a solution of the system. 1. (5, ) 1. x + y = 7 x y = 3. ( 1, ). x + y = 5 x
More informationAlgebra I Practice Exam
Algebra I This practice assessment represents selected TEKS student expectations for each reporting category. These questions do not represent all the student expectations eligible for assessment. Copyright
More information28 (Late Start) 7.2a Substitution. 7.1b Graphing with technology Feb 2. 4 (Late Start) Applications/ Choosing a method
Unit 7: Systems of Linear Equations NAME: The calendar and all assignments are subject to change. Students will be notified of any changes during class, so it is their responsibility to pay attention and
More informationWhy? Speed Skating Tracks offi cial track short track
Applying Systems of Linear Equations Then You solved systems of equations by using substitution and elimination. (Lessons 6-2, 6-3, and 6-4) Now 1Determine the best method for solving systems of 2Apply
More informationAlgebra 2 Level 2 Summer Packet
Algebra Level Summer Packet This summer packet is for students entering Algebra Level for the Fall of 01. The material contained in this packet represents Algebra 1 skills, procedures and concepts that
More informationName Algebra 1 Midterm Review Period. = 10 4x e) x ) Solve for y: a) 6x 3y = 12 b) 4y 8x = 16
Name Algebra 1 Date Midterm Review Period 1) Solve each equation: a) x 2x + 2 = 3 b) 5 5 + 9 = 13 c) 64 = 9x +1 d) x 7 2 = 10 4x e) x + 2 3 = 3x 2) Solve for y: a) 6x 3y = 12 b) 4y 8x = 16 3) Solve and
More informationIntensive Math-Algebra I Mini-Lesson MA.912.A.3.1
Intensive Math-Algebra I Mini-Lesson MA.912.A.3.1 Summer 2013 Solving Linear Equations Student Packet Day 3 Name: Date: Benchmark MA.912.A.3.1 Solve linear equations in one variable that include simplifying
More informationUnit 12: Systems of Equations
Section 12.1: Systems of Linear Equations Section 12.2: The Substitution Method Section 12.3: The Addition (Elimination) Method Section 12.4: Applications KEY TERMS AND CONCEPTS Look for the following
More information6 which of the following equations would give you a system of equations with the same line and infinitely many solutions?
Algebra 1 4 1 Worksheet Name: Per: Part I: Solve each system of equations using the graphing method. 1) y = x 5 ) -x + y = 6 y = x + 1 y = -x 3) y = 1 x 3 4) 4x y = 8 y = 1 x + 1 y = x + 3 5) x + y = 6
More informationUNIT 5 INEQUALITIES CCM6+/7+ Name: Math Teacher:
UNIT 5 INEQUALITIES 2015-2016 CCM6+/7+ Name: Math Teacher: Topic(s) Page(s) Unit 5 Vocabulary 2 Writing and Graphing Inequalities 3 8 Solving One-Step Inequalities 9 15 Solving Multi-Step Inequalities
More informationName Class Date. Essential question: How do you interpret, evaluate and write algebraic expressions that model real-world situations?
Name Class Date 1-1 1 Variables and Expressions Going Deeper Essential question: How do you interpret, evaluate and write algebraic expressions that model real-world situations? A-SSE.1.1a ENGAGE Interpreting
More informationSystems of Equations Unit Five ONE NONE INFINITE
Systems of Equations Unit Five ONE NONE INFINITE Standards: 8.EE.8 Analyze and solve pairs of simultaneous linear equations. a. Understand that solutions to a system of two linear equations in two variables
More informationUnit Test Linear equations and Inequalities
Unit Test Linear equations and Inequalities Name: Date: Directions: Select the best answer for the following questions. (2 points each) 7L 1. The steps for solving are: 1) Read the problem and label variables,
More informationAlgebra I. Systems of Linear Equations and Inequalities. Slide 1 / 179. Slide 2 / 179. Slide 3 / 179. Table of Contents
Slide 1 / 179 Algebra I Slide 2 / 179 Systems of Linear Equations and Inequalities 2015-04-23 www.njctl.org Table of Contents Slide 3 / 179 Click on the topic to go to that section 8th Grade Review of
More information8 th Grade Domain 2: Algebra and Functions (40%) Sara
8 th Grade Domain 2: Algebra and Functions (40%) 1. Tara creates a budget for her weekly expenses. The graph shows how much money is in the account at different times. Find the slope of the line and tell
More information1. What are the various types of information you can be given to graph a line? 2. What is slope? How is it determined?
Graphing Linear Equations Chapter Questions 1. What are the various types of information you can be given to graph a line? 2. What is slope? How is it determined? 3. Why do we need to be careful about
More informationUnit 6 Systems of Equations
1 Unit 6 Systems of Equations General Outcome: Develop algebraic and graphical reasoning through the study of relations Specific Outcomes: 6.1 Solve problems that involve systems of linear equations in
More informationApplications of Systems of Equations
Applications of Systems of Equations Procedure for Solving Application Problems. 1. Read the problem carefully. 2. Determine the unknowns and assign variable(s) to them. 3. Set up your equation(s). 4.
More informationMath 803. Unit 1: Solving Equations in One Variable (8.EE.7) Part 2
Math 803 Unit 1: Solving Equations in One Variable (8.EE.7) Part 2 1.4 Variables on both sides (2.4 text) 1.5 Solve multi-step equations (2.5 text) Name: Period: Teacher s Name: 1 Lesson 1.4 Equations
More informationThe Top 11 Keystones of Algebra 1
The Top 11 Keystones of Algebra 1 The Top Eleven Keystones of Algebra 1 You should be able to 1) Simplify a radical expression. 2) Solve an equation. 3) Solve and graph an inequality on a number line.
More informationName Date PD. Systems of Equations and Inequalities
Name Date PD Sstems of Equations and Inequalities Sstems of Equations Vocabular: A sstem of linear equations is A solution of a sstem of linear equations is Points of Intersection (POI) are the same thing
More informationGrade 8. Functions 8.F.1-3. Student Pages
THE NEWARK PUBLIC SCHOOLS THE OFFICE OF MATHEMATICS Grade 8 Functions 8.F.1-3 Student Pages 2012 2012 COMMON CORE CORE STATE STATE STANDARDS ALIGNED ALIGNED MODULES Grade 8 - Lesson 1 Introductory Task
More informationFoundations of Math. Chapter 3 Packet. Table of Contents
Foundations of Math Chapter 3 Packet Name: Table of Contents Notes #43 Solving Systems by Graphing Pg. 1-4 Notes #44 Solving Systems by Substitution Pg. 5-6 Notes #45 Solving by Graphing & Substitution
More informationSolve each absolute value equation x 7 = x 9 = (3x 12) = - 12
Solve each absolute value equation. 16. 3x 7 = 11 17. - 4 x 9 = - 16 18. 2(3x 12) = - 12 19. Explain why there can be one, two or no solutions to an absolute value equation. 5. Solve each equation for
More information3.3 Solving Systems with Elimination
3.3 Solving Systems with Elimination Sometimes it is easier to eliminate a variable entirely from a system of equations rather than use the substitution method. We do this by adding opposite coefficients
More informationa. Bob: 7, Bridget: 4, Brian 1 b. Bob: 7, Bridget: 4, Brian 3 c. Bob: 7, Bridget: 14, Brian 3 a. 100 b. 150 c c. 2 d.
Period: Date: K. Williams 8th Grade Year Review: Chapters -4. A neighborhood pool charges $22 for a pool membership plus an additional $2 for each visit to the pool. If Elliot visited the pool 6 times,
More informationReady To Go On? Skills Intervention 2-1 Solving Equations by Adding or Subtracting
Ready To Go On? Skills Intervention 2-1 Solving Equations by Adding or Subtracting Find these vocabulary words in Lesson 2-1 and the Multilingual Glossary. Vocabulary equation solution of an equation Solve
More informationAlgebra I Chapter 6 Practice Test
Name: Class: Date: ID: A Algebra I Chapter 6 Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. Find a solution of the system of linear inequalities.
More information5-1 Solving Inequalities by Addition and Subtraction. Solve each inequality. Then graph the solution set on a number line. 1.
5-1 Solving Inequalities by Addition and Subtraction Solve each inequality Then graph the solution set on a number line 1 x 3 > 7 The solution set is {p p 7} 5 10 > n 1 The solution set is {x x > 10} The
More informationEquations can be classified according to the types of operations and quantities involved. Important types include:
UNIT 5. EQUATIONS AND SYSTEM OF EQUATIONS EQUATIONS An equation is a mathematical statement that asserts the equality of two expressions. In modern notation, this is written by placing the expressions
More informationPre-Test Unit 5: Solving Equations KEY
Pre-Test Unit 5: Solving Equations KEY No calculator necessary. Please do not use a calculator. Solve the following equations for the given variable. There may be a single solution, infinite solutions,
More informationUnit 5 Test Review Systems of Linear Equations Name Class Date
Unit 5 Test Review Systems of Linear Equations Name Class Date Find the mistake - The following problems have been solved HOWEVER there could be a mistake. Each question is worth 3 points: 1pt the mistake,
More informationName Class Date. Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved.
Practice - Solving Two-Step Equations Solve each equation. Check your answer.. a +. +. b +. 9 + t. a +. -t + Write an equation to model each situation. Then solve.. You want to buy a bouquet of yellow
More informationFall IM I Exam B
Fall 2011-2012 IM I Exam B Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which of the following equations is linear? a. y = 2x - 3 c. 2. What is the
More informationSystems of Linear Equations
HW Mark: 10 9 8 7 6 RE-Submit Systems of Linear Equations This booklet belongs to: Period LESSON # DATE QUESTIONS FROM NOTES Questions that I find difficult Pg. Pg. Pg. Pg. Pg. Pg. Pg. Pg. Pg. Pg. REVIEW
More information6th Grade. Dependent & Independent Variables
Slide 1 / 68 Slide 2 / 68 6th Grade Dependent & Independent Variables 2014-10-28 www.njctl.org Slide 3 / 68 Table of Contents Translating to Equations Dependent and Independent Variables Click on a topic
More informationAlgebra 1 Midterm Review
Name Block Algebra 1 Midterm Review MULTIPLE CHOICE Write the letter for the correct answer at the left of each question. 1. Solve: A. 8 C. 2. Solve: A. 43 C. 42 3. Solve the compound inequality and graph
More informationHow can you use linear functions of two independent variables to represent problem situations?
Problems that occur in business situations often require expressing income as a linear function of one variable like time worked or number of sales. For example, if an employee earns $7.25 per hour, then
More informationSection 4 Topic 1 Arithmetic Sequences
Section 4 Topic 1 Arithmetic Sequences Let s look at the following sequence of numbers: 3, 8, 13, 18, 23,.... Ø Ø Ø The at the end means that this sequence goes on forever. 3, 8, 13, 18, and 23 are the
More informationConsistent and Dependent
Graphing a System of Equations System of Equations: Consists of two equations. The solution to the system is an ordered pair that satisfies both equations. There are three methods to solving a system;
More informationMathematics Department Columbia High School. Advanced Algebra 2 Summer Packet
Mathematics Department Columbia High School Advanced Algebra Summer Packet This summer packet is for students entering Advanced Algebra (10-5) for the Fall. The material contained in this packet represents
More informationLecture Guide. Math 42 - Elementary Algebra. Stephen Toner. Introductory Algebra, 3rd edition. Miller, O'Neill, Hyde. Victor Valley College
Lecture Guide Math 42 - Elementar Algebra to accompan Introductor Algebra, 3rd edition Miller, O'Neill, Hde Prepared b Stephen Toner Victor Valle College Accompaning videos can be found at www.mathvideos.net.
More informationIndiana Core 40 End-of-Course Assessment Algebra I Blueprint*
Types of items on the Algebra I End-of-Course Assessment: Multiple-choice 1 point per problem The answer to the question can be found in one of four answer choices provided. Numeric response 1 point per
More informationCCGPS Coordinate Algebra. EOCT Review Units 1 and 2
CCGPS Coordinate Algebra EOCT Review Units 1 and 2 Unit 1: Relationships Among Quantities Key Ideas Unit Conversions A quantity is a an exact amount or measurement. A quantity can be exact or approximate
More informationAlgebra I. Systems of Linear Equations and Inequalities. 8th Grade Review. Slide 1 / 179 Slide 2 / 179. Slide 4 / 179. Slide 3 / 179.
Slide 1 / 179 Slide 2 / 179 lgebra I Systems of Linear Equations and Inequalities 2015-04-23 www.njctl.org Slide 3 / 179 Table of Contents Click on the topic to go to that section 8th Grade Review of Systems
More information4. The table shows the number of toll booths driven through compared to the cost of using a Toll Tag.
ALGEBRA 1 Fall 2016 Semester Exam Review Name 1. According to the data shown below, which would be the best prediction of the average cost of a -bedroom house in Georgetown in the year 2018? Year Average
More informationApplications of Systems of Linear Equations
5.2 Applications of Systems of Linear Equations 5.2 OBJECTIVE 1. Use a system of equations to solve an application We are now ready to apply our equation-solving skills to solving various applications
More informationAlgebra 1 PAP Fall Exam Review
Name: Pd: 2016-2017 Algebra 1 PAP Fall Exam Review 1. A collection of nickels and quarters has a value of $7.30. The value of the quarters is $0.80 less than triple the value of the nickels. Which system
More informationArkansas Council of Teachers of Mathematics Algebra I Regional Exam Spring 2008
Arkansas Council of Teachers of Mathematics Algebra I Regional Exam Spring 008 Select the best answer for each of the following questions and mark it on the answer sheet provided. Be sure to read all the
More informationAlgebra I Final Study Guide
2011-2012 Algebra I Final Study Guide Short Answer Source: www.cityoforlando.net/public_works/stormwater/rain/rainfall.htm 1. For which one month period was the rate of change in rainfall amounts in Orlando
More informationSystems of Linear Equations: Solving by Adding
8.2 Systems of Linear Equations: Solving by Adding 8.2 OBJECTIVES 1. Solve systems using the addition method 2. Solve applications of systems of equations The graphical method of solving equations, shown
More informationName Period Date DRAFT
Name Period Date Equations and Inequalities Student Packet 4: Inequalities EQ4.1 EQ4.2 EQ4.3 Linear Inequalities in One Variable Add, subtract, multiply, and divide integers. Write expressions, equations,
More informationAlgebra 1 Unit 6: Linear Inequalities and Absolute Value Guided Notes
Section 6.1: Solving Inequalities by Addition and Subtraction How do we solve the equation: x 12 = 65? How do we solve the equation: x 12 < 65? Graph the solution: Example 1: 12 y 9 Example 2: q + 23
More informationName Class Date. You can use the properties of equality to solve equations. Subtraction is the inverse of addition.
2-1 Reteaching Solving One-Step Equations You can use the properties of equality to solve equations. Subtraction is the inverse of addition. What is the solution of + 5 =? In the equation, + 5 =, 5 is
More informationSolve Problems with Equations
Develop Skills and Strategies Part 1: Introduction Solve Problems with Equations CCSS 7.EE.B. 7.EE.B.4a You know how to compute with rational numbers and write and solve one-step equations. Take a look
More informationSimple Inequalities Involving Addition and Subtraction. Unit 3 Inequalities.notebook. November 18, Table of Contents
Table of Contents Simple Inequalities Addition/Subtraction Simple Inequalities Multiplication/Division Two-Step and Multiple-Step Inequalities Solving Compound Inequalities Special Cases of Compound Inequalities
More informationMath 1 Unit 7 Review
Name: ate: 1. Which ordered pair is the solution to this system of equations? 5. system of equations is graphed on the set of axes below. y = x + 4 x + y = 2. (1, 5). (0, 2). ( 1, 3). ( 4, 0) 2. Which
More information4) Solve for this system using your graphing
Algebra Unit 5 HW Day 1 SOLVING GRAPHICALLY Graph the following systems: 1) x 2y 12 y 2x 6 2) y x 2 6x 2y 10 ) x y 9 4) Solve for this system using your graphing x calculator. [You will still need to put
More informationAlgebra 1 Keystone Remediation Packet Module 1 Anchor 2
Algebra 1 Keystone Remediation Packet Module 1 Anchor 2 A.1.1.2.1.1 Write, solve, and/or graph linear equations using various methods. A.1.1.2.1.2 Use and/or identify an algebraic property to justify any
More informationAlgebra II Honors Summer Review (150 problems) Part 1 Equations and Inequalities
Algebra II Honors Summer Review (150 problems) Part 1 Equations and Inequalities Simplify each expression. 1. 25+14 17 6 2. 6+12 12 9 3. 52+3 25 7 4. 10 43+7+6 5. 9 +14 17+6 8 6. 52+3+8 6 7. 3+9 12 + 8.
More informationAlgebra I Solving & Graphing Inequalities
Slide 1 / 182 Slide 2 / 182 Algebra I Solving & Graphing Inequalities 2016-01-11 www.njctl.org Slide 3 / 182 Table of Contents Simple Inequalities Addition/Subtraction click on the topic to go to that
More information4. Based on the table below, what is the joint relative frequency of the people surveyed who do not have a job and have a savings account?
Name: Period: Date: Algebra 1 Common Semester 1 Final Review Like PS4 1. How many surveyed do not like PS4 and do not like X-Box? 2. What percent of people surveyed like the X-Box, but not the PS4? 3.
More informationMr. Gallo Algebra 2 1 2: PROPERTIES OF REAL NUMBERS. Real Number Review
Mr. Gallo Algebra 2 1 2: PROPERTIES OF REAL NUMBERS Real Number Review 1 Subsets of the Real Numbers Classifying Variables Example 1: What set of numbers would best describe the number of participants
More informationSkills Practice Skills Practice for Lesson 5.1
Skills Practice Skills Practice for Lesson. Name Date Widgets, Dumbbells, and Dumpsters Multiple Representations of Linear Functions Vocabular Write the term that best completes each statement.. A(n) is
More informationIM1: UNIT 3. HOMEWORK PACKET
IM1: UNIT 3. HOMEWORK PACKET Week 1 Name: Period: Day 1: Write an equation for each situation. Then solve the equation. Show your work. 1) DVDs bought online cost $12 each, plus a shipping fee of $5. The
More informationSHOW ALL WORK ON SEPARATE PAPER Answers will be provided at a later date. REAL NUMBER SYSTEM Go back and try problems on Review 1 and Test 1.
07 Accelerated Fall Exam Review Name: SHOW ALL WORK ON SEPARATE PAPER Answers will be provided at a later date. REAL NUMBER SYSTEM Go back and try problems on Review and Test.. Name the set(s) of numbers
More informationAlgebra 1 STAAR EOC Review #7 Reporting Category 4: Linear Equations and Inequalities
Name Class Date RC3 A.07A Algebra 1 STAAR EOC Review #7 Reporting Category 4: Linear Equations and Inequalities 1. Passengers on many commercial flights may make calls from a telephone provided by the
More informationThis is Solving Linear Systems, chapter 4 from the book Beginning Algebra (index.html) (v. 1.0).
This is Solving Linear Systems, chapter 4 from the book Beginning Algebra (index.html) (v. 1.0). This book is licensed under a Creative Commons by-nc-sa 3.0 (http://creativecommons.org/licenses/by-nc-sa/
More information3.1 NOTES Solving Systems of Linear Equations Graphically
3.1 NOTES Solving Systems of Linear Equations Graphically A system of two linear equations in two variables x and y consist of two equations of the following form: Ax + By = C Equation 1 Dx + Ey = F Equation
More informationWhy? Step 3 Substitute the value from Step 2 into either equation, and solve for the other variable. Write the solution as an ordered pair.
Substitution Then You solved systems of equations by graphing. (Lesson 6-1) Now 1Solve systems of equations by using substitution. 2Solve real-world problems involving systems of equations by using substitution.
More informationBenchmark Test : Grade 6 Math. Class/Grade. Benchmark: MA.6.A.3.2. Which inequality best represents the graph below? A x 4 B x 4 C x 4 D x 4
Name ClassGrade Date Benchmark: MA..A.. Which inequality best represents the graph below? A x B x C x D x Benchmark: MA..A.. What is another way to write ( ) ( )? F ( ) ( ) G ( ) ( ) H ( ) ( ) I ( ) (
More informationspring98a Math A Regents Exam Test Sampler spring ) ) 2.5
spring98a For what value of x will 8 and x have the same mean (average) as 27 and 5? ).5 2) 8 3) 24 4) 40 6 Which is a factor of x 2 + 5x 24? ) (x + 4) 2) (x 4) 3) (x + 3) 4) (x 3) 2 If 2x = 4(x + 5),
More information4.7 Solutions of Rational Equations
www.ck1.org Chapter 4. Rational Equations and Functions 4.7 s of Rational Equations Learning Objectives Solve rational equations using cross products. Solve rational equations using lowest common denominators.
More information8-3 Writing Equations
Translate each sentence into an equation. 1. The quotient of a number and 3, less 8, is 16. Translate each sentence into an equation. 7. Eighteen more than half a number is 8. 2. Tiffani spent $95 for
More information1. The sum of four consecutive even numbers is 52. What is the largest of these numbers?
1. The sum of four consecutive even numbers is 52. What is the largest of these numbers? 26 22 C 16 10 2. In a high school basketball game, Sarah scored 10 points in the first half of the game. In the
More informationUnit 4: Inequalities. Inequality Symbols. Algebraic Inequality. Compound Inequality. Interval Notation
Section 4.1: Linear Inequalities Section 4.2: Solving Linear Inequalities Section 4.3: Solving Inequalities Applications Section 4.4: Compound Inequalities Section 4.5: Absolute Value Equations and Inequalities
More informationSection 2.1 Objective 1: Determine If a Number Is a Solution of an Equation Video Length 5:19. Definition A in is an equation that can be
Section 2.1 Video Guide Linear Equations: The Addition and Multiplication Properties of Equality Objectives: 1. Determine If a Number Is a Solution of an Equation 2. Use the Addition Property of Equality
More informationOregon Focus on Linear Equations Lesson 1 Answers
Lesson 1 Answers 1. a. Nathan; multiplication b. Subtraction 2. 30 3. 28 4. 40 5. 17 6. 29 7. 21 8. 7 9. 4 10. 33 11. 8 12. 1 13. 5 14. 19 15. 12 16. 15 17. a. 130 5 + 40 8 b. $970 18. a. (11 + 8 + 13)
More informationMore with Systems of Equations
More with Systems of Equations In 2008, 4.7 million Americans went on a rafting expedition. In Georgia, outfitters run whitewater expeditions for ages 8 and up on the Chattooga River. 12.1 Systems of Equations
More informationEvaluate and Simplify Algebraic Expressions
TEKS 1.2 a.1, a.2, 2A.2.A, A.4.B Evaluate and Simplify Algebraic Expressions Before You studied properties of real numbers. Now You will evaluate and simplify expressions involving real numbers. Why? So
More information2-4. Warm Up Lesson Presentation Lesson Quiz
Warm Up Lesson Presentation Lesson Quiz Holt Algebra McDougal 1 Algebra 1 Warm Up Solve each equation. 1. 2x 5 = 17 6 2. 14 Solve each inequality and graph the solutions. 3. 5 < t + 9 t > 4 4. a 8 Objective
More informationMath 1 Variable Manipulation Part 4 Word Problems
Math 1 Variable Manipulation Part 4 Word Problems 1 TRANSLATING FROM ENGLISH INTO ALGEBRA (PLUG IN) The next part of variable manipulation problems is to figure out the problem from real life situations.
More informationWriting and Solving Equations
Writing and Solving Equations Melody s Music Solution Lesson 6-1 Modeling and Writing Two-Step Equations ACTIVITY 6 Learning Targets: Use variables to represent quantities in real-world problems. Model
More informationDue for this week. Slide 2. Copyright 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
MTH 209 Week 1 Due for this week Homework 1 (on MyMathLab via the Materials Link) Monday night at 6pm. Read Chapter 6.1-6.4, 7.1-7.4,10.1-10.3,10.6 Do the MyMathLab Self-Check for week 1. Learning team
More information4. Based on the table below, what is the joint relative frequency of the people surveyed who do not have a job and have a savings account?
Name: Period: Date: Algebra 1 Common Semester 1 Final Review 1. How many surveyed do not like PS4 and do not like X-Box? 2. What percent of people surveyed like the X-Box, but not the PS4? 3. What is the
More informationTo determine the slope or rate of change of a linear function, use m =, positive slopes, rises from left to right, negative
Common Core Regents Review Linear Functions The standard form for a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept. To determine the slope or rate of change
More informationc. Solve the system of two equations to find the speed of the boat in the water (x) and the speed of the current (y). (0.45, 0.05)
Math Applications The applications that follow are like the ones you will encounter in many workplaces. Use the mathematics you have learned in this chapter to solve the problems. Wherever possible, use
More informationCC Math I UNIT 7 Systems of Equations and Inequalities
CC Math I UNIT 7 Systems of Equations and Inequalities Name Teacher Estimated Test Date MAIN CONCEPTS Page(s) Study Guide 1 2 Equations of Circles & Midpoint 3 5 Parallel and Perpendicular Lines 6 8 Systems
More information