Lesson 17 Section 3.1 System of Equations (in 2 variables)
|
|
- Spencer Bradford
- 5 years ago
- Views:
Transcription
1 Lesson 17 Section 3.1 System of Equations (in 2 variables) A System of Equations (in 2 variables) is a set of two equations in two variables for which a common solution is sought. A Solution of such a system is an ordered pair that makes both equations true. I Determining is a given ordered pair is a solution of a System 1. Replace each equation with the correct values from the ordered pair. 2. If both are true, that ordered pair is a solution. Determine if the given ordered pair is a solution of the system shown. 4x y = 9 1) (1, -5) x 3y = 16 2) (-1, -2) x + 3y = 7 3x 2y = 12 3) (3, 1) 3x + 4y = 13 6x + 8y = 26 1
2 II Solving a System of Equation (in 2 variables) Graphically 1. Graph each equation by an appropriate method you have learned a) Plotting general points b) Plotting the intercepts c) Using slope and y-intercept d) Graphing a vertical or horizontal line 2. Locate the ordered pair where the graphs intersect Solve each system graphically. 3x + y = 5 4) x 2y = 4 (Let s graph these lines by changing the equations to slope-intercept form, then using the slope and y-intercept to graph.) Solution: 2
3 a b = 1 5) 2a + b = 5 (Let s graph these lines by plotting the intercepts.) a 0 a 0 b 0 b 0 Solution: 3
4 6) 2x 3y = 6 y = 2 x 2 3 7) If two lines were parallel, how would you describe the solution of the system? If a system of equations in two variables has a solution, we say the system is Consistent. If a system of equation has no solution, we say the system is Inconsistent. If the equations of the lines of a system represent different lines, then the equations are said to be Independent. If the system s equations represent the same line, then the equations are said to be Dependent (really same equation). Here is a summary of the definitions above and what each means graphically. A Lines intersect at one point; system is consistent (solution is one ordered pair) and equations are independent (different lines). 4
5 B Lines are parallel; system is inconsistent (no solution) and equations are independent (different lines). C Line is the same for each equation; system is consistent (solution is an infinite number of ordered pairs) and equations are dependent (same line). Using a System of Equations of 2 Variables to translate an Application Problem For the lessons over section 1.4, we translated word problems (application problems) to an equation. However, we only used one equation with one variable. Sometimes it is easier or necessary to use two variables. In this case, we must write two equations. For each problem, define two variables and write two equations. (We will not solve these, just write the equations.) 1) The sum of two numbers is 40. The first number is 10 more than the second number. What are the numbers? 1 st number: 2 nd number: 2) In , the average total SAT score for high school students was 1026, with the average math score exceeding the verbal score by 12 points. What were the average math score and average verbal score on the SAT for that year? *Source: College Entrance Examination Board Average math score: Average verbal score: 5
6 3) Two angles are complementary, have a sum of 90 degrees. The sum of the measures of the first angle and half the second angle is 64 degrees. Find the measures of the angles. 1 st angle: 2 nd angle: 4) Recently an art club purchased 120 stamps for $46. If the stamps were a combination of $0.43 and $0.29 stamps, how many of each type were bought? # $0.43 stamps: #$0.29 stamps: 5) In 2003 Americans bought an average of 76.4 gallons of water and soft drinks per person. The amount of water per person was only 4.3 gallons less that half of the amount of soft drinks per person. How many gallons of each did the average American buy that year? Source: Data from Gallons of water: Gallons of soft drinks: 6) A Community College Basketball Squad recently made 40 field goals in a game, some 2-pointers and the rest 3-pointers. These field goals amounted to 89 points. How many of each kind of field goal was made? # 2-pointers: # 3-pointers: 6
7 7) A Community Center served 250 dinners at a Charity event. A child s plate cost $3.50 and an adult s plate cost $7.00. If the Center raised $ from these dinners, how many of each type of plate was served? # child plates: # adult plates: 8) Diana furniture outlet regularly sells two popular types of dinette sets; one is in oak and the other in walnut. In July, the outlet sold 5 of the oak sets and 4 of the walnut and collected $18,400 from the sales of these dinette sets. In August, they sold 2 of the oak and 6 of the walnut and collected $17,980. What is the price of each type of dinette set? Price for Oak set: Price for Walnut set: 9) The perimeter of a standard tennis court used for doubles is 228 feet. The width is 42 feet less than the length. Find the dimensions. Width: Length: 7
Math 10 - Unit 8 REVIEW WORKSHEET - Systems of Linear Equations
Class: Date: Math 10 - Unit 8 REVIEW WORKSHEET - Systems of Linear Equations Multiple Choice Identify the choice that best answers the question. 1. Without graphing, determine the equation whose graph
More informationSections 8.1 & 8.2 Systems of Linear Equations in Two Variables
Sections 8.1 & 8.2 Systems of Linear Equations in Two Variables Department of Mathematics Porterville College September 7, 2014 Systems of Linear Equations in Two Variables Learning Objectives: Solve Systems
More informationWarm Up. Unit #1: Basics of Algebra
1) Write an equation of the given points ( 3, 4) & (5, 6) Warm Up 2) Which of the following choices is the Associative Property 1) 4(x + 2) = 4x + 8 2) 4 + 5 = 5 + 4 3) 5 + ( 5) = 0 4) 4 + (3 + 1) = (4
More informationGraphing Systems of Linear Equations
Graphing Systems of Linear Equations Groups of equations, called systems, serve as a model for a wide variety of applications in science and business. In these notes, we will be concerned only with groups
More informationName Class Date. Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. Travels in Air. Distance (miles) Time (seconds)
Practice - Rate of Change and Slope Find the slope of each line.... O O O Find the slope of the line that passes through each pair of points.. (, ), (7, 5) 5. (8, ), (, ). (, 5), (, 7) 7. (-, 7), (, -)
More informationMathematics Level D: Lesson 2 Representations of a Line
Mathematics Level D: Lesson 2 Representations of a Line Targeted Student Outcomes Students graph a line specified by a linear function. Students graph a line specified by an initial value and rate of change
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 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 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 informationSolve Linear Systems Algebraically
TEKS 3.2 a.5, 2A.3.A, 2A.3.B, 2A.3.C Solve Linear Systems Algebraically Before You solved linear systems graphically. Now You will solve linear systems algebraically. Why? So you can model guitar sales,
More information3-3 Using Tables and Equations of Lines
3-3 Using Tables and Equations of Lines Objectives Students will understand that linear models are appropriate when the situation has a constant increase/decrease. slope is the rate of change. the rate
More informationMath 3 Variable Manipulation Part 7 Absolute Value & Inequalities
Math 3 Variable Manipulation Part 7 Absolute Value & Inequalities 1 MATH 1 REVIEW SOLVING AN ABSOLUTE VALUE EQUATION Absolute value is a measure of distance; how far a number is from zero. In practice,
More informationChapter 4. Systems of Linear Equations; Matrices. Opening Example. Section 1 Review: Systems of Linear Equations in Two Variables
Chapter 4 Systems of Linear Equations; Matrices Section 1 Review: Systems of Linear Equations in Two Variables Opening Example A restaurant serves two types of fish dinners- small for $5.99 and large for
More informationEquations With Two or More Variables
! Equations With Two or More Variables You have done a lot of work with relationships involving two related variables. However, many real-world relationships involve three or more variables. For example,
More informationCORE. Chapter 3: Interacting Linear Functions, Linear Systems. Algebra Assessments
CORE Algebra Assessments Chapter 3: Interacting Linear Functions, Linear Systems 97 98 Bears Band Booster Club The Bears Band Booster Club has decided to sell calendars to the band members and their parents.
More informationLinear Systems and Matrices. Copyright Cengage Learning. All rights reserved.
7 Linear Systems and Matrices Copyright Cengage Learning. All rights reserved. 7.1 Solving Systems of Equations Copyright Cengage Learning. All rights reserved. What You Should Learn Use the methods of
More informationChapter 4. Systems of Linear Equations; Matrices
Chapter 4 Systems of Linear Equations; Matrices Section 1 Review: Sys of Linear Eg in Two Var Section 2 Sys of Linear Eq and Aug Matr Section 3 Gauss-Jordan Elimination Section 4 Matrices: Basic Operations
More information1.8 Multi-Step Inequalities
1.8 Multi-Step Inequalities Learning Objectives Solve a two-step inequality. Solve a multi-step inequality. Identify the number of solutions of an inequality. Solve real-world problems using inequalities.
More informationChapter 4. Inequalities
Chapter 4 Inequalities Vannevar Bush, Internet Pioneer 4.1 Inequalities 4. Absolute Value 4.3 Graphing Inequalities with Two Variables Chapter Review Chapter Test 64 Section 4.1 Inequalities Unlike equations,
More informationMath 10 Lesson 5-1 System of Linear Equations Graphical solution
Math 10 Lesson 5-1 System of Linear Equations Graphical solution I. Lesson Objectives: 1) Use the graphs of the equations of a linear system to estimate its solution. 2) Learn how to write a system of
More informationExample Items. Algebra I Pre-AP
Example Items Algebra I Pre-AP Algebra I Pre-AP Example Items are a representative set of items for the ACP. Teachers may use this set of items along with the test blueprint as guides to prepare students
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 informationMATH 1710 College Algebra Final Exam Review
MATH 1710 College Algebra Final Exam Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) There were 480 people at a play.
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 informationCHAPTER 8 Quadratic Equations, Functions, and Inequalities
CHAPTER Quadratic Equations, Functions, and Inequalities Section. Solving Quadratic Equations: Factoring and Special Forms..................... 7 Section. Completing the Square................... 9 Section.
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 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 informationUnit 7: It s in the System
Unit 7: It s in the System Investigation 1: Linear Equations with Two Variables I can convert between standard and slope intercept forms, and graph systems of equations. Solving equations is one of the
More informationStudent Name: End-of-Course Assessment. Algebra II. Algebra 2 Pre-Test
Student Name: End-of-Course Assessment Algebra II Algebra Pre-Test 1. What is the expanded form of. Which equation can be used to find the nth term for the sequence below?, 5, 10, 17,... t = n + 3 t =
More informationName Period Date Ch. 5 Systems of Linear Equations Review Guide
Reteaching 5-1 Solving Systems by Graphing ** A system of equations is a set of two or more equations that have the same variables. ** The solution of a system is an ordered pair that satisfies all equations
More informationGraphical Solutions of Linear Systems
Graphical Solutions of Linear Systems Consistent System (At least one solution) Inconsistent System (No Solution) Independent (One solution) Dependent (Infinite many solutions) Parallel Lines Equations
More informationCreate your own system of equations: 1. Prove (2, 5) is a solution for the following system: 2. Is (-2, 0) a solution for the following system?
5.1 Explain Solving Systems of Linear Equations by Graphing - Notes Main Ideas/ Questions What You Will Learn What is a system of linear equations? Essential Question: How can you solve a system of linear
More informationPre-IB Geometry Summer Assignment
Pre-IB Geometry Summer Assignment This summer assignment is for all incoming freshman in the IB program, whom will begin their math course of study with Pre-IB Geometry. All work must be completed in pencil,
More informationMath 135 Intermediate Algebra. Homework 3 Solutions
Math Intermediate Algebra Homework Solutions October 6, 007.: Problems,, 7-. On the coordinate plane, plot the following coordinates.. Next to each point, write its coordinates Clock-wise from upper left:
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 informationThe steps in Raya s solution to 2.5 (6.25x + 0.5) = 11 are shown. Select the correct reason for line 4 of Raya s solution.
A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear functions. Unit 2: Reasoning with Linear Equations and Inequalities The perimeter
More informationElementary Algebra Review for Exam 4
Elementary Algebra Review for Eam 4 ) The length of a rectangular picture frame is 9 cm more than the width. The area inside the frame is 90 square cm. Find the dimensions of the frame. ) A 0-ft ladder
More informationChapter 9 Solving Systems of Linear Equations Algebraically
Name: Chapter 9 Solving Systems of Linear Equations Algebraically 9.1 Solving Systems of Linear Equations by Substitution Outcomes: 1. Interpret algebraic reasoning through the study of relations 9. Solve
More information5-3B Systems Review Puzzle
5-3B Systems Review Puzzle x + y = 4 x y = -2 2x + y = -4 2x + 3y = 4 2x + y = 1 4x 2y = 6 2x + y = 1 x + y = 1 3x 2y = 4-2x + 2y = -1 x = -2y + 1 4 = x + y y = 2 2x x = y 5 y = 4 + 3x 2x + 1 = y x y =
More informationThe Method of Substitution. Linear and Nonlinear Systems of Equations. The Method of Substitution. The Method of Substitution. Example 2.
The Method of Substitution Linear and Nonlinear Systems of Equations Precalculus 7.1 Here is an example of a system of two equations in two unknowns. Equation 1 x + y = 5 Equation 3x y = 4 A solution of
More informationAdvAlg5.3SolvingSystemsBySubstitution.notebook February 26, 2018
Oct 14 4:53 PM 1 Why do we need algebraic techniques to solve systems? To find exact solutions The substitution method for solving systems of equations uses what property of equality? Substitution property
More informationDefinition: A "system" of equations is a set or collection of equations that you deal with all together at once.
System of Equations Definition: A "system" of equations is a set or collection of equations that you deal with all together at once. There is both an x and y value that needs to be solved for Systems
More informationLesson 28: Another Computational Method of Solving a Linear System
Lesson 28: Another Computational Method of Solving a Linear System Student Outcomes Students learn the elimination method for solving a system of linear equations. Students use properties of rational numbers
More informationKEYSTONE ALGEBRA I REVIEW
1. Which graph represents a linear function 4. The faces of a cube are numbered from 1 to 6. If the cube is tossed once, what is the probability that a prime number or a number divisible by 2 is obtained
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 information10-1: Composite and Inverse Functions
Math 95 10-1: Composite and Inverse Functions Functions are a key component in the applications of algebra. When working with functions, we can perform many useful operations such as addition and multiplication
More informationAlgebra - Chapter 5 Review
Name Hour Algebra - Chapter 5 Review 1. Write an equation in slope-intercept form of the graph. 10 y 10 x 10 2. The cost of a school banquet is $95 plus $15 for each person attending. Write an equation
More informationWoodland Community College: Math Practice Test
Woodland Communit College: Math Practice Test Elementar Algebra Math Test The following problems are recommended practice problems for the elementar algebra section of the placement test. Some of the problems
More informationLinear Relations and Functions
Linear Relations and Functions Why? You analyzed relations and functions. (Lesson 2-1) Now Identify linear relations and functions. Write linear equations in standard form. New Vocabulary linear relations
More informationSystems of Equations and Inequalities
1 Systems of Equations and Inequalities 2015 03 24 2 Table of Contents Solving Systems by Graphing Solving Systems by Substitution Solve Systems by Elimination Choosing your Strategy Solving Systems of
More informationOTHER METHODS FOR SOLVING SYSTEMS
Topic 18: Other methods for solving systems 175 OTHER METHODS FOR SOLVING SYSTEMS Lesson 18.1 The substitution method 18.1 OPENER 1. Evaluate ab + 2c when a = 2, b = 3, and c = 5. 2. Following is a set
More informationPre-Test. Name Date. 3 3 x 5 5. Solve each equation. 2. 2x x
Pre-Test Name Date 1. The equation 3x 2 4 5 11 is solved as shown. Describe the inverse operations used in each step. 3x 2 4 5 11 Step 1: 3x 2 4 1 4 5 11 1 4 3x 5 15 Step 2: 3x 5 15 3 3 x 5 5 Solve each
More informationChapter 7 Linear Systems and Matrices
Chapter 7 Linear Systems and Matrices Overview: 7.1 Solving Systems of Equations 7.2 Systems of Linear Equations in Two Variables 7.3 Multivariable Linear Systems 7.1 Solving Systems of Equations What
More informationALGEBRA 1 UNIT 3 WORKBOOK CHAPTER 6
ALGEBRA 1 UNIT 3 WORKBOOK CHAPTER 6 FALL 2014 0 1 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
More informationGrade 9 Ch. 6 Test Review Equations & Inequalities
Grade 9 Ch. 6 Test Review Equations & Inequalities Name:_ Multiple Choice: Identify the choice that best completes the statement or answers the question. 1. Solve: a. 8 b. 8 c. 3 d. 3 2. Solve: a. 0.4
More informationPre-Test Chapter
Pre-Test Name Date 1. The equation 3x 2 11 is solved as shown. Describe the inverse operations used in each step. 3x 2 11 Step 1: 3x 2 1 11 1 3x 1 Step 2: 3x 1 3 x In Step 1, was added to both sides of
More informationPre-Algebra Chapter 8 Linear Functions and Graphing
Pre-Algebra Chapter 8 Linear Functions and Graphing SOME NUMBERED QUESTIONS HAVE BEEN DELETED OR REMOVED. YOU WILL NOT BE USING A CALCULATOR FOR PART I MULTIPLE-CHOICE QUESTIONS, AND THEREFORE YOU SHOULD
More informationThe Keystones of Algebra 1
The Keystones of Algebra 1 The Top Ten 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. 4) Manipulate
More informationSTA Summer Review for Students Entering Algebra 3
Alg Summer Review STA Summer Review for Students Entering Algebra This packet will be collected and graded the first week of school. There will also be a test over this material the first week of school.
More information4.4 Problem Solving Using Systems of Equations
4.4 Problem Solving Using Systems of Equations Steps 1) Read, read, read. Draw a diagram, if needed. 2) Assign a variable to each unknown (need 2 variables). 3) Translate so you have 2 equations. 4) Solve
More information3-4 Equations of Lines
Write an equation in slope-intercept form of the line having the given slope and y-intercept. Then graph the line. 1. m: 4, y-intercept: 3 3. y-intercept: 5 y = 4x 3 2. y-intercept: 1 Write an equation
More informationLesson 12: Systems of Linear Equations
Our final lesson involves the study of systems of linear equations. In this lesson, we examine the relationship between two distinct linear equations. Specifically, we are looking for the point where the
More informationChapter 1 Analytic Geometry
Chapter 1 Analytic Geometry 1. Find the coordinates of the midpoint of the line segment AB whose endpoints are A(5, 4) and B(-3, -4) 2. N (-2, 1) and D (8, 5) are the endpoints of the diameter of a circle.
More informationName: Class: Date: ID: A
Name: Class: Date: 8th Grade Advanced Topic III, Linear Equations and Systems of Linear Equations, MA.8.A.1.1, MA.8.1.1.2, MA.8.A.1.3, *MA.8.A.1.4, MA.8.A.1.5, MA.8.A.1.6 Multiple Choice Identify the choice
More informationAlgebra 2/Trigonometry Summer Review Packet
Algebra 2/Trigonometry Summer Review Packet This packet is designed to help you review the mathematical topics that you will need to be successful at AOSR. To receive full points for this required packet,
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 information3.1 Solving Linear Systems by Graphing 1. Graph and solve systems of linear equations in two variables. Solution of a system of linear equations
3.1 Solving Linear Systems by Graphing Objectives 1. Graph and solve systems of linear equations in two variables. Key Terms System of linear equations Solution of a system of linear equations Check whether
More informationUNIT 5: Systems of Equations
Algebra 2 Trig UNIT 5: Systems of Equations Name: Teacher: Pd: 1 Table of Contents Day 1: Review Solving Linear Systems SWBAT: Solve linear systems algebraically and graphically. Homework: Page 7 Day 2:
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 informationGraphing Linear Equations and Inequalities
Algebra I Name: Date: Period: # Graphing Linear Equations and Inequalities Linear Equation/Inequalities equations/inequalities that will be represented using lines on the coordinate plane. Assignments
More informationALGEBRA 1 FINAL EXAM TOPICS
ALGEBRA 1 FINAL EXAM TOPICS Chapter 2 2-1 Writing Equations 2-2 Solving One Step Equations 2-3 Solving Multi-Step Equations 2-4 Solving Equations with the Variable on Each Side 2-5 Solving Equations Involving
More informationInequalities Chapter Test
Inequalities Chapter Test Part 1: For questions 1-9, circle the answer that best answers the question. 1. Which graph best represents the solution of 8 4x < 4 A. B. C. D. 2. Which of the following inequalities
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 informationAssignments for Algebra 1 Unit 4: Linear Functions and Correlation
Name: Assignments for Algebra 1 Unit 4: Linear Functions and Correlation Day Date Assignment (Due the next class meeting) Thursday 10/25/12 (A) Monday 10/29/12 (B) 4.1 Worksheet Tuesday 10/30/12 (A) Wednesday
More informationEssential Question How can you use substitution to solve a system of linear equations?
5.2 Solving Systems of Linear Equations by Substitution Essential Question How can you use substitution to solve a system of linear equations? Using Substitution to Solve Systems Work with a partner. Solve
More informationSY14-15 Algebra Exit Exam - PRACTICE Version
Student Name: Directions: Solve each problem. You have a total of 90 minutes. Choose the best answer and fill in your answer document accordingly. For questions requiring a written response, write your
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 informationAlgebra. Chapter 6: Systems of Equations and Inequalities. Name: Teacher: Pd:
Algebra Chapter 6: Systems of Equations and Inequalities Name: Teacher: Pd: Table of Contents Chapter 6-1: SWBAT: Identify solutions of systems of linear equations in two variables; Solve systems of linear
More informationSolve each system by graphing. Check your solution. y =-3x x + y = 5 y =-7
Practice Solving Sstems b Graphing Solve each sstem b graphing. Check our solution. 1. =- + 3 = - (1, ). = 1 - (, 1) =-3 + 5 3. = 3 + + = 1 (, 3). =-5 = - 7. = 3-5 3 - = 0 (1, 5) 5. -3 + = 5 =-7 (, 7).
More information= (1 3 )= =4 3 +2=4. Now that we have it down to a simple two-step equation, we can solve like normal and get the following: =4 2
6.3 Solving Systems with Substitution While graphing is useful for an estimate, the main way that we can solve a system to get an exact answer is algebraically. There are a few useful methods to do this,
More information12/14/2010. Directions
Directions You will have 4 minutes to answer each question. The scoring will be 16 points for a correct response in the 1 st minute, 12 points for a correct response in the 2 nd minute, 8 points for a
More informationPRACTICE FOR PLACEMENT EXAM PART A
PRACTICE FOR PLACEMENT EXAM PART A For students trying to place into: MAT 099, Intermediate Algebra MAT 000, Mathematics in Today s World MAT 00, Algebra with Trigonometry Problems - are based on Arithmetic
More informationHolt Algebra 1. Know-It Notebook TM
Holt Algebra 1 Know-It Notebook TM Copyright by Holt, Rinehart and Winston No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including
More informationAlgebra 1 Third Quarter Study Guide
Algebra 1 Third Quarter Study Guide 1. Evaluate:. 2. Evaluate: 8 5 5 t. 2 s t when s = 5 and 7 Simplify. 3. 2 0 5 3 2x y x y 4. 4 3 54xy 5. 4 24 6. 3x 2 y 3 7. Is 3 a solution of? 8. A store that sells
More informationWhy? Sport. Source: The National Federation of State High School Associations. The element -1 is in Row 2, Column 1. 4 columns.
Organizing Data Using Matrices Then You represented data using statistical graphs. (Lesson -) Now Organize data in matrices. Perform matrix operations. Why? The table shows high school participation in
More informationChapter 6: Exploring Data: Relationships Lesson Plan
Chapter 6: Exploring Data: Relationships Lesson Plan For All Practical Purposes Displaying Relationships: Scatterplots Mathematical Literacy in Today s World, 9th ed. Making Predictions: Regression Line
More informationMATH 080 Final-Exam Review
MATH 080 Final-Exam Review Can you simplify an expression using the order of operations? 1) Simplify 32(11-8) - 18 3 2-3 2) Simplify 5-3 3-3 6 + 3 A) 5 9 B) 19 9 C) - 25 9 D) 25 9 Can you evaluate an algebraic
More informationMATH 021 TEST 3 REVIEW SHEET
TO THE STUDENT: MATH 021 TEST 3 REVIEW SHEET This Review Sheet gives an outline of the topics covered on Test 3 as well as practice problems. Answers for all problems begin on page 8. In several instances,
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 informationMATH FOR LIBERAL ARTS FINAL REVIEW
MATH FOR LIBERAL ARTS FINAL REVIEW Find the value of the annuity. Round to the nearest cent. A = P 1 + r n r n nt - 1 P = A r n 1 + r n nt - 1 1) Periodic Deposit: $100 at the end of each year Rate: 5%
More informationRate of Change and slope. Objective: To find rates of change from tables. To find slope.
Linear Functions Rate of Change and slope Objective: To find rates of change from tables. To find slope. Objectives I can find the rate of change using a table. I can find the slope of an equation using
More informationALGEBRA 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 informationStandard 5.1 Pre-Assessment 2
Standard 5. Pre-Assessment Name: Date: For #-9, decide the number of solutions for each system of linear equations below. A. Solution B. No solution C. Infinitely Many Solutions... 4. x + y = x + y = 5.
More informationProgress Assessment Mid U3 (PAMU3) This chart shows some of the bonus points awarded for different numbers of points accumulated.
Name: Date: 1. A student is playing a video game. At the end of each level of the game she is awarded bonus points based on the number of points she has accumulated. This chart shows some of the bonus
More informationFoundations of Algebra. Learning Goal 3.1 Algebraic Expressions. a. Identify the: Variables: Coefficients:
Learning Goal 3.1 Algebraic Expressions What you need to know & be able to do 1. Identifying Parts of Algebraic Expressions 3.1 Test Things to remember Identify Parts of an expression Variable Constant
More informationCoordinate Algebra A Final Exam Review
Class: Date: Coordinate Algebra A Final Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. Do NOT write on the test. You may use your calculator.
More informationChapter 3 Test, Form 1
Chapter 3 Test, Form 1 Write the letter for the correct answer in the blank at the right of each question. 1. Where does the graph of y = 3x 18 intersect the x-axis? A (0, 6) B (0, 6) C (6, 0) D ( 6, 0)
More informationAlgebra I Midterm Exam Review
Chapter 1: Expressions, Equations, and Functions Lesson 1.1 Variables and Expressions Write a verbal expression for each algebraic expression. 23f 5m 2 + 2c 3 4n 1 7 Write an algebraic expression for each
More informationLesson 1: Writing Equations Using Symbols
COMMON CORE MATHEMATICS CURRICULUM Lesson 1 8 4 Lesson 1: Writing Equations Using Symbols Classwork Exercises Write each of the following statements using symbolic language. 1. The sum of four consecutive
More informationName Period Date. ** A system of equations is a set of two or more equations that have the same variables.
Reteaching 5-1 Solving Systems by Graphing ** A system of equations is a set of two or more equations that have the same variables. ** The solution of a system is an ordered pair that satisfies all equations
More information