1. Graph the system of equations and tell the solution. 1. Solution

Size: px
Start display at page:

Download "1. Graph the system of equations and tell the solution. 1. Solution"

Transcription

1 Algebra Reporting Strand 4: Systems of Equations & Inequalities Subunit 4a: Solving Systems of Equations Review Name: Period: Date: Read all the directions carefully, put your answers in the blanks provided, and SHOW YOUR WORK!!! NO WORK = NO CREDIT CCSS 4-Mastery 3-Proficient 2-Basic 1-Below Basic 0-No Evidence Solve Systems of Equations (A.REI.6, A.CED.2, A.CED.4) Meets all of the criteria in a Level 3 Completes tasks including synthesis and evaluation or in context of a new situation Solve a system of linear equations in two variables using all of following methods: Graphing (standard form) Substitution Elimination (both equations need to be multiplied) Solve a system of linear equations in two variables using all of following methods: Graphing (slope intercept form) Substitution Elimination (one equation needs to be multiplied) Solve a system of linear equations in two variables using 2 of following methods: Graphing (slope intercept form) Substitution (one variable solved for) Elimination Little evidence of reasoning or application to solve the problem Does not meet the criteria in a level 1 1. Graph the system of equations and tell the solution. 1. Solution 3x y = 2 4y = x + 5

2 Solve each system by graphing. 2. y= 3x+7 x+ 1 2 y=1 3. x+2y=0 3x+2y= y 2x=1 y=2x+6 5. y=x+3 y=5x

3 Solve each system using substitution. 6. 2x y= 8 3x y= 9 4x 2y= x y= x=y+2 2y=1 3x 9. x=2y 2 3y=x

4 Solve each system using elimination x+5y=16 3x 5y= x y=4 9x+y= x+y=9 x+2y=11 3x= 18+4y y=58+5x

5 14. 8x+4y=20 7x+6y= x 8y= 22 5x 3y= Given the equation 3x + 9y = 8, write a second linear equation to create a system that: a. Has exactly one solution. Explain your reasoning. b. Has no solution. Explain your reasoning. c. Has infinitely many solutions. Explain your reasoning.

6 17. Interpret the meaning of the solution, if it exists, in the context of the graph of the following systems of equations. 5x + 2y = 10 10x 4y = A theaters charges $9 for each adult ticket & $6 for each children ticket. The theater sold 144 tickets for the first showing of a new released movie. The total money collected from tickets sales for that show was $1,164. Write a system of equations that could be used to find the number of children tickets and the number of adult tickets sold, and solve the system algebraically. Solution: 19. Tim has a collection of 12 CDs and Nina has a collection of 18 CDs. Tim is adding 4 CDs a month to his collection while Nina is adding 3 CDs a month to her collection. Write a system to describe this situation. Then find the number of months after which they will have the same number of CDs. Solution:

7 20. A corner store sells two kinds of baked goods: cakes and pies. A cake costs $4 and a pie costs $9. In one day, the store sold 13 baked goods for a total of $87. Write a system to describe this situation. Then find out how many cakes and pies did they sell? Solution: 21. At the local ballpark, the team charges $5 for each ticket and expects to make $1,200 in concessions. The team must pay its players $1,900 and pay all other workers $1,400. Each fan gets a free bat that costs the team $1 per bat. How many tickets must be sold to break even? Solution: 22. Denise has $1.95 in her pocket made up of 27 nickels and dimes. How many of each type of coin does she have? Solution:

Alg 1 Systems. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

Alg 1 Systems. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question. Class: Date: Alg 1 Systems Multiple Choice Identify the choice that best completes the statement or answers the question. What is the solution of the system? Use a graph. 1. y = x + 2 y = 3x 1 a. c. b.

More information

Algebra I Chapter 6 Practice Test

Algebra 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 information

Lesson 12: Systems of Linear Equations

Lesson 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 information

Algebra. Chapter 6: Systems of Equations and Inequalities. Name: Teacher: Pd:

Algebra. 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 information

BOROUGH OF MANHATTAN COMMUNITY COLLEGE DEPARTMENT OF MATHEMATICS MAT 051 Midterm Examination Review

BOROUGH OF MANHATTAN COMMUNITY COLLEGE DEPARTMENT OF MATHEMATICS MAT 051 Midterm Examination Review BOROUGH OF MANHATTAN COMMUNITY COLLEGE DEPARTMENT OF MATHEMATICS MAT 051 Midterm Examination Review Do ONLY 4 CHAPTERS. Your instructor will tell you which 4 chapters to complete. Everyone is required

More information

Unit 12: Systems of Equations

Unit 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 information

Topic 1. Solving Equations and Inequalities 1. Solve the following equation

Topic 1. Solving Equations and Inequalities 1. Solve the following equation Topic 1. Solving Equations and Inequalities 1. Solve the following equation Algebraically 2( x 3) = 12 Graphically 2( x 3) = 12 2. Solve the following equations algebraically a. 5w 15 2w = 2(w 5) b. 1

More information

Algebra 2 Summer Review Packet

Algebra 2 Summer Review Packet Algebra Summer Review Packet Welcome to Algebra! Attached you will find the learning targets your teacher thinks you should know BEFORE you come to class in the fall and problems to help you practice these

More information

Common Core Algebra Rock the Regents Station 1:Linear Equations & Inequalities. Name: Teacher: Date: Grade: (circle one) Period:

Common Core Algebra Rock the Regents Station 1:Linear Equations & Inequalities. Name: Teacher: Date: Grade: (circle one) Period: Common Core Algebra Rock the Regents 2016 Station 1:Linear Equations & Inequalities Name: Teacher: Date: Grade: 9 10 11 12 (circle one) Period: Topic: Modeling Expressions Tips/Hints Look for keywords/hints

More information

ALGEBRA 1 FINAL EXAM TOPICS

ALGEBRA 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 information

Unit 7 Systems and Linear Programming

Unit 7 Systems and Linear Programming Unit 7 Systems and Linear Programming PREREQUISITE SKILLS: students should be able to solve linear equations students should be able to graph linear equations students should be able to create linear equations

More information

ALGEBRA MIDTERM REVIEW SHEET

ALGEBRA MIDTERM REVIEW SHEET Name Date Part 1 (Multiple Choice): Please show ALL work! ALGEBRA MIDTERM REVIEW SHEET 1) The equations 5x 2y 48 and 3x 2y 32 represent the money collected from school concert ticket sales during two class

More information

Name Class Date. What is the solution to the system? Solve by graphing. Check. x + y = 4. You have a second point (4, 0), which is the x-intercept.

Name Class Date. What is the solution to the system? Solve by graphing. Check. x + y = 4. You have a second point (4, 0), which is the x-intercept. 6-1 Reteaching Graphing is useful for solving a system of equations. Graph both equations and look for a point of intersection, which is the solution of that system. If there is no point of intersection,

More information

6 which of the following equations would give you a system of equations with the same line and infinitely many solutions?

6 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 information

Inequalities Chapter Test

Inequalities 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 information

Unit 5 SIMULTANEOUS LINEAR EQUATIONS

Unit 5 SIMULTANEOUS LINEAR EQUATIONS MATH 8 Unit 5 SIMULTANEOUS LINEAR EQUATIONS By the end of this unit, students should be able to: 1. Solve simultaneous linear equations by graphing. 2. Understand what it means to solve a system of equations.

More information

Name. 1. Given the solution (3, y), what is the value of y if x + y = 6? 7. The graph of y = x 2 is shown below. A. 3 B. 4 C. 5 D.

Name. 1. Given the solution (3, y), what is the value of y if x + y = 6? 7. The graph of y = x 2 is shown below. A. 3 B. 4 C. 5 D. Name 1. Given the solution (, y), what is the value of y if x + y = 6? 7. The graph of y = x is shown below. 5 D. 6. What are the solutions to the equation x - x = 0? x = - or x = - x = - or x = 1 x =

More information

ECM Final Exam Review

ECM Final Exam Review Name: Date: 1. Which of the following is the graph of the solution set of the system? y 2 y x 3 2. Three times a number n is greater than 8 more than the number. Which of the following inequalities best

More information

BOROUGH OF MANHATTAN COMMUNITY COLLEGE DEPARTMENT OF MATHEMATICS MAT 012/051 Final Examination Review Form H. Multiple Choice Problems

BOROUGH OF MANHATTAN COMMUNITY COLLEGE DEPARTMENT OF MATHEMATICS MAT 012/051 Final Examination Review Form H. Multiple Choice Problems BOROUGH OF MANHATTAN COMMUNITY COLLEGE DEPARTMENT OF MATHEMATICS MAT 012/051 Final Examination Review Form H Multiple Choice Problems 1. If a = -1 and b = -2, find the value of!3a2 b + 2b 3 a. a) -2 b)

More information

Algebra I Review **You may use a calculator throughout the review with the exception of Part A and Part B.

Algebra I Review **You may use a calculator throughout the review with the exception of Part A and Part B. Algebra I Review **You may use a calculator throughout the review with the exception of Part A and Part B. Part A Find the value of each expression below No calculator! 1) ( 7) ) 7 3) 4 1 8 6 3 4 4) 459

More information

Algebra 1 PAP Fall Exam Review

Algebra 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 information

Foundations of Math. Chapter 3 Packet. Table of Contents

Foundations 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 information

Consistent and Dependent

Consistent 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 information

Students will develop an understanding of linear equations and inequalities (including systems of each) and apply related solution techniques.

Students will develop an understanding of linear equations and inequalities (including systems of each) and apply related solution techniques. Grade: Algebra I Enduring Skill 1: Students will develop an understanding of linear equations and inequalities (including systems of each) and apply related solution techniques. Demonstrators and Related

More information

Study Guide and Review - Chapter 6

Study Guide and Review - Chapter 6 State whether each sentence is or false. If false, replace the underlined term to make a sentence. 1. If a system has at least one solution, it is said to be consistent. Graph each system and determine

More information

b. In the situation described above, what is the value of y?

b. In the situation described above, what is the value of y? 1 Algebra I Chapter 6 Test Review Standards/Goals: D.1.g: I can solve systems of equations in a variety of methods, including: graphing, substitution and elimination. A.REI.12.: I can graph the solution

More information

y z ). Write all solutions using only positive

y z ). Write all solutions using only positive 1. a) Graph the equation x y =. b) What is the x-intercept? What is the y-intercept? d) What is the slope of this line?. a) Find the slope of the line joining the points and ( b) Find the equation of this

More information

Checkpoint 1 Simplifying Like Terms and Distributive Property

Checkpoint 1 Simplifying Like Terms and Distributive Property Checkpoint 1 Simplifying Like Terms and Distributive Property Simplify the following expressions completely. 1. 3 2 2. 3 ( 2) 3. 2 5 4. 7 3 2 3 2 5. 1 6 6. (8x 5) + (4x 6) 7. (6t + 1)(t 2) 8. (2k + 11)

More information

Algebra 1 Midterm Review

Algebra 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 information

Chapter 7: Systems of Linear Equations

Chapter 7: Systems of Linear Equations Chapter 7: Systems of Linear Equations Section 7.1 Chapter 7: Systems of Linear Equations Section 7.1: Developing Systems of Linear Equations Terminology: System of Linear Equations: A grouping of two

More information

How can you use linear functions of two independent variables to represent problem situations?

How 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 information

7.1 Solving Systems of Equations

7.1 Solving Systems of Equations Date: Precalculus Notes: Unit 7 Systems of Equations and Matrices 7.1 Solving Systems of Equations Syllabus Objectives: 8.1 The student will solve a given system of equations or system of inequalities.

More information

You solved systems of equations algebraically and represented data using matrices. (Lessons 0-5 and 0-6)

You solved systems of equations algebraically and represented data using matrices. (Lessons 0-5 and 0-6) You solved systems of equations algebraically and represented data using matrices. (Lessons 0-5 and 0-6) Solve systems of linear equations using matrices and Gaussian elimination. Solve systems of linear

More information

Algebra 1 Fall Final Review

Algebra 1 Fall Final Review 1.) (A.5A) Solve: 3(2x 1) + 12 = 4x + 1 5.) (A.2.) Write the equation of the line below: Y= 2.) (A.5A) Aaron and Kim are bowling. Kim s score Is twice the difference of Aaron s score and 5. The sum of

More information

Chapter Systems of Equations

Chapter Systems of Equations SM-1 Name: 011314 Date: Hour: Chapter 6.1-6.4 Systems of Equations 6.1- Solving Systems by Graphing CCS A.REI.6: Solve systems of equations exactly and approximately (e.g. with graphs), focusing on pairs

More information

due test Prerequisite Skills for Algebra II Advanced

due test Prerequisite Skills for Algebra II Advanced Name: Student ID: Algebra II Advanced is a very rigorous and fast-paced course. In order to prepare for the rigor of this course, you will need to be familiar with the topics in this packet prior to starting

More information

45 Minutes 27 Questions YOU MAY WRITE ON THIS

45 Minutes 27 Questions YOU MAY WRITE ON THIS Algebra 2 Chapter 3.3/3.4 Review NAME 45 Minutes 27 Questions YOU MAY WRITE ON THIS DIRECTIONS: Solve each problem, choose the correct answer, and then fill in the corresponding oval on your answer document.

More information

NOTES. [Type the document subtitle] Math 0310

NOTES. [Type the document subtitle] Math 0310 NOTES [Type the document subtitle] Math 010 Cartesian Coordinate System We use a rectangular coordinate system to help us map out relations. The coordinate grid has a horizontal axis and a vertical axis.

More information

Chapter 9. Lesson 9.1.1

Chapter 9. Lesson 9.1.1 Chapter 9 Lesson 9.1.1 9-2. a. Inequalities have multiple solutions, but equalities only have one solution. b. infinite c. The result of 1 x 4 does not extend infinitely. It has two endpoints. The result

More information

Coordinate Algebra A Final Exam Review

Coordinate 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 information

For the given equation, first find the x-intercept by setting y = 0: Next, find the y-intercept by setting x = 0:

For the given equation, first find the x-intercept by setting y = 0: Next, find the y-intercept by setting x = 0: 1. Find the x- and y-intercepts and graph the equation. 5x + 6y = 30 To find the x- and y-intercepts, set one variable equal to 0, and solve for the other variable. To find the x-intercept, set y = 0 and

More information

October 5 th October 9 th. Unit 2: Equations & Inequalities

October 5 th October 9 th. Unit 2: Equations & Inequalities Algebra I: Week 6 Math Packet October 5 th October 9 th Unit 2: Equations & Inequalities Jump Start Directions: Answer the Regents question below to the best of your ability. Solve the inequality below

More information

0-2. 2) Plot the points and connect them. X

0-2. 2) Plot the points and connect them. X 1) Pam s Pie Pantry had 2 backorders for cherry pies. Pam can bake 3 pies every hour. Fill in the blanks. Hours 0-2 Pies Practice 6C 2) Plot the points and connect them. 3) Write an equation for the line.

More information

PreAP Algebra 2 Unit 1 and Unit 2 Review Name A#

PreAP Algebra 2 Unit 1 and Unit 2 Review Name A# PreAP Algebra Unit and Unit Review Name A# Domain and Range:. The graph of the square root function f is shown below. - - - - - - - - - - Interval Notation Domain: Range: Inequalit Notation Domain: Range:.

More information

Name Period Date Ch. 5 Systems of Linear Equations Review Guide

Name 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 information

Here are the exams I wrote when teaching Math 115 in Fall 2018 at Ferris State University. Each exam is followed by its solutions.

Here are the exams I wrote when teaching Math 115 in Fall 2018 at Ferris State University. Each exam is followed by its solutions. Here are the exams I wrote when teaching Math 5 in Fall 208 at Ferris State University. Each exam is followed by its solutions. Fall 208 Exam. (a) Find the slope of the line passing through the points

More information

Math 4: Advanced Algebra Ms. Sheppard-Brick B Quiz Review Learning Targets

Math 4: Advanced Algebra Ms. Sheppard-Brick B Quiz Review Learning Targets 5B Quiz Review Learning Targets 4.6 5.9 Key Facts We learned two ways to solve a system of equations using algebra: o The substitution method! Pick one equation and solve for either x or y! Take that result

More information

Skills Practice Skills Practice for Lesson 2.1

Skills Practice Skills Practice for Lesson 2.1 Skills Practice Skills Practice for Lesson.1 Name Date Finding a Job Introduction to Systems of Linear Equations Vocabulary Write the term that best completes each statement. 1. A(n) is the location on

More information

Foundations of Algebra. Learning Goal 3.1 Algebraic Expressions. a. Identify the: Variables: Coefficients:

Foundations 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 information

Unit 5 Review Systems of Linear Equations and Inequalities

Unit 5 Review Systems of Linear Equations and Inequalities Unit 5 Review Systems of Linear Equations and Inequalities Name: Algebra 1B Day 1: Solutions to Systems and Solving by Graphing Warm Up: Determine if the point (2,5) is a solution to each of the systems

More information

Elementary Algebra SAMPLE Final Examination Spring 2015

Elementary Algebra SAMPLE Final Examination Spring 2015 Elementary Algebra NAME: SAMPLE Final Examination Spring 2015 You will have 2 hours to complete this exam. You may use a calculator but must show all algebraic work in the space provided to receive full

More information

Unit 6 Systems of Equations

Unit 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 information

Math 10 - Unit 8 REVIEW WORKSHEET - Systems of Linear Equations

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 information

Elementary Algebra Review for Exam 4

Elementary Algebra Review for Exam 4 Elementary Algebra Review for Exam 4 List all numbers for which the rational expression is undefined. 9 ) a - 7 2) 3) x2-25 x2 + 2x + 32 x2-49 x2-3x - 40 Simplify, if possible. 4) 2m 6p2 4m9p 5) 6) x +

More information

Pre-Algebra Chapter 2 Solving One-Step Equations and Inequalities

Pre-Algebra Chapter 2 Solving One-Step Equations and Inequalities Pre-Algebra Chapter 2 Solving One-Step Equations and Inequalities SOME NUMBERED QUESTIONS HAVE BEEN DELETED OR REMOVED. YOU WILL NOT BE USING A CALCULATOR FOR PART I MULTIPLE-CHOICE QUESTIONS, AND THEREFORE

More information

Algebra 2 Semester 1 Exam Review Multiple Choice

Algebra 2 Semester 1 Exam Review Multiple Choice Algebra Semester Exam Review Multiple Choice Chapter. (No Calculator) Which list shows the numbers in decreasing order.7,,,,,,.,. 7 7 7 C.,,,,. 7,.,.7, 7 7. Which of the following statements illustrates

More information

Final Exam Study Guide

Final 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 information

Algebra I. Systems of Linear Equations and Inequalities. Slide 1 / 179. Slide 2 / 179. Slide 3 / 179. Table of Contents

Algebra 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 information

ALGEBRA 1 UNIT 12: SYSTEMS OF LINEAR EQUATIONS

ALGEBRA 1 UNIT 12: SYSTEMS OF LINEAR EQUATIONS Key Dates ALGEBRA 1 UNIT 12: SYSTEMS OF LINEAR EQUATIONS Quiz: Block Day, February 19-20, 2014 Test: Tuesday, February 25, 2014 Day 1 (Monday, February 17, 2014) Solving Systems of Equations through Graphing

More information

Math Studio College Algebra

Math Studio College Algebra Math 100 - Studio College Algebra Rekha Natarajan Kansas State University November 19, 2014 Systems of Equations Systems of Equations A system of equations consists of Systems of Equations A system of

More information

Algebra 1 Third Quarter Study Guide

Algebra 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 information

due Thursday, August 25, Friday, September 2, 2016 test Prerequisite Skills for Algebra II Advanced

due Thursday, August 25, Friday, September 2, 2016 test Prerequisite Skills for Algebra II Advanced Name: Student ID: Algebra II Advanced is a very rigorous and fast-paced course. In order to prepare for the rigor of this course, you will need to be familiar with the topics in this packet prior to starting

More information

Chapter 1-2 Add and Subtract Integers

Chapter 1-2 Add and Subtract Integers Chapter 1-2 Add and Subtract Integers Absolute Value of a number is its distance from zero on the number line. 5 = 5 and 5 = 5 Adding Numbers with the Same Sign: Add the absolute values and use the sign

More information

Algebra Unit 6 Test review white boards notea.notebook. February 02, y = y = a) (-3, -2) b) (1, -3) c) (0, -1) c) (2, 3) a) ( 1, 3) d) ( 3, 1)

Algebra Unit 6 Test review white boards notea.notebook. February 02, y = y = a) (-3, -2) b) (1, -3) c) (0, -1) c) (2, 3) a) ( 1, 3) d) ( 3, 1) Unit 6 white board review 1. Find the solution to the graph on the right. ( 1, 3) (3, 1) c) (2, 3) d) ( 3, 1) Graph and find the point of intersection for each. 2. (-3, -2) (1, -3) c) (0, -1) 3. Graph

More information

BETHLEHEM CATHOLIC HIGH SCHOOL

BETHLEHEM CATHOLIC HIGH SCHOOL BETHLEHEM CATHOLIC HIGH SCHOOL ALGEBRA SUMMER ASSIGNMENT NAME: - Variables and Expressions For Exercises, choose the correct letter.. The word minus corresponds to which symbol? A. B. C. D.. The phrase

More information

Addition and Subtraction of real numbers (1.3 & 1.4)

Addition and Subtraction of real numbers (1.3 & 1.4) Math 051 lecture notes Professor Jason Samuels Addition and Subtraction of real numbers (1.3 & 1.4) ex) 3 + 5 = ex) 42 + 29 = ex) 12-4 = ex) 7-9 = ex) -3-4 = ex) 6 - (-2) = ex) -5 - (-3) = ex) 7 + (-2)

More information

NON-CALCULATOR: I. Decide whether or not the following information defines a function. Explain/support your answer x y

NON-CALCULATOR: I. Decide whether or not the following information defines a function. Explain/support your answer x y NON-CALCULATOR: I. Decide whether or not the following information defines a function. Explain/support your answer. 1. 2. 3. x -1 0 1 2 3 y 5 7 2-1 -8 4 & 5. Refer to the numbered graphs 4 5 6. x -3 2

More information

5-3B Systems Review Puzzle

5-3B 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 information

Key Vocabulary. Vocabulary Check. 4. If a system has no solution, it is said to be inconsistent. 7. Each number in a matrix is called a(n) dimension.

Key Vocabulary. Vocabulary Check. 4. If a system has no solution, it is said to be inconsistent. 7. Each number in a matrix is called a(n) dimension. Study Guide and Review Study Guide Key Concepts Systems of Equations (Lessons - through -4) A system with a graph of two intersecting lines has one solution and is consistent and independent. Graphing

More information

Exam: RR - SYSTEMS OF EQUATIONS; INEQUALITIES. 1. Graph the inequality y 3.

Exam: RR - SYSTEMS OF EQUATIONS; INEQUALITIES. 1. Graph the inequality y 3. Exam: 050291RR - SYSTEMS OF EQUATIONS; INEQUALITIES When you have completed your exam and reviewed your answers, click Submit Exam. Answers will not be recorded until you hit Submit Exam. If you need to

More information

Systems of Equations and Inequalities

Systems 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 information

Semester One Review. FORMULAS Given on Exam! 3. What is the value of f(5), given the equation f(x) = x 2 4x + 1? Slope:

Semester One Review. FORMULAS Given on Exam! 3. What is the value of f(5), given the equation f(x) = x 2 4x + 1? Slope: FORMULAS Given on Exam!. What is equivalent to A. -(x )? B. (x + ) (x + ). Evaluate: A. + 7 B. C.. D.. = i. 6.6 ii. 6.6 iii. 6 iv. 6 E. + F. 0 + G. 9. ( ) H. ( + ) + ( + ) I. ( ) + = J. 9x 0 + y (when

More information

Intro. To Graphing Linear. Equations

Intro. To Graphing Linear. Equations The Coordinate Plane Intro. To Graphing Linear A. The coordinate plane has 4 quadrants. Equations B. Each point in the coordinate plain has an x-coordinate (the abscissa) and a y-coordinate (the ordinate).

More information

ALLEN PARK HIGH SCHOOL First Semester Review

ALLEN PARK HIGH SCHOOL First Semester Review Algebra Semester Review Winter 0 ALLEN PARK HIGH SCHOOL First Semester Review Algebra Winter 0 Algebra Semester Review Winter 0 Select the best answer for all 8 questions. Please show all work (or attach

More information

Keystone Exam Concept Review. Properties and Order of Operations. Linear Equations and Inequalities Solve the equations. 1)

Keystone Exam Concept Review. Properties and Order of Operations. Linear Equations and Inequalities Solve the equations. 1) Keystone Exam Concept Review Name: Properties and Order of Operations COMMUTATIVE Property of: Addition ASSOCIATIVE Property of: Addition ( ) ( ) IDENTITY Property of Addition ZERO PRODUCT PROPERTY Let

More information

Systems of Linear Equations: Solving by Adding

Systems 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 information

REVIEW Algebra 1 Fall Final

REVIEW Algebra 1 Fall Final 1. (A.5A) Solve: 4(x 8) = 4x (7x 3) A. x = 29/7 B. x = 5 C. x = no solution D. x = 5 Use the graph below to answer questions #2-3 6. (A.2E) Write the equation of a line passing through ( 5, 7)that is parallel

More information

South Brunswick Schools

South Brunswick Schools South Brunswick Schools Summer Packet For Rising Honors Algebra students Directions: All students entering Honors Algebra are expected to be proficient in all their previously-learned algebra and geometry

More information

1. What are the various types of information you can be given to graph a line? 2. What is slope? How is it determined?

1. 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 information

Algebra 1R REVIEW (midterm)

Algebra 1R REVIEW (midterm) Algebra 1R Algebra 1R REVIEW (midterm) Short Answer 1. Find the x- and y-intercepts. 2. Tara creates a budget for her weekly expenses. The graph shows how much money is in the account at different times.

More information

Vocabulary REVIEW BLOCK y = 1_ 2x x + 4y = x + 3y = y = 2x 1 8. x 3y = 4 9. y = x 2

Vocabulary REVIEW BLOCK y = 1_ 2x x + 4y = x + 3y = y = 2x 1 8. x 3y = 4 9. y = x 2 REVIEW elimination method parallel rational numbers Vocabulary BLOCK 4 solution to a system of linear equations substitution method system of linear equations Lesson 4. ~ Parallel, Intersecting or The

More information

4-5 Scatter Plots Plots and and Trend Lines

4-5 Scatter Plots Plots and and Trend Lines 4-5 Scatter Plots Plots and and Trend Lines Warm Up Lesson Presentation Lesson Quiz Holt Holt Algebra Algebra 1 1 The image cannot be displayed. Your computer may not have enough memory to open the image,

More information

MATH 080 Final-Exam Review

MATH 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 information

Intermediate Algebra Semester Summary Exercises. 1 Ah C. b = h

Intermediate Algebra Semester Summary Exercises. 1 Ah C. b = h . Solve: 3x + 8 = 3 + 8x + 3x A. x = B. x = 4 C. x = 8 8 D. x =. Solve: w 3 w 5 6 8 A. w = 4 B. w = C. w = 4 D. w = 60 3. Solve: 3(x ) + 4 = 4(x + ) A. x = 7 B. x = 5 C. x = D. x = 4. The perimeter of

More information

ALGEBRA UNIT 5 LINEAR SYSTEMS SOLVING SYSTEMS: GRAPHICALLY (Day 1)

ALGEBRA UNIT 5 LINEAR SYSTEMS SOLVING SYSTEMS: GRAPHICALLY (Day 1) ALGEBRA UNIT 5 LINEAR SYSTEMS SOLVING SYSTEMS: GRAPHICALLY (Day 1) System: Solution to Systems: Number Solutions Exactly one Infinite No solution Terminology Consistent and Consistent and Inconsistent

More information

Name Algebra 1 Midterm Review Period. = 10 4x e) x ) Solve for y: a) 6x 3y = 12 b) 4y 8x = 16

Name 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 information

ALGEBRA 1. Unit 3 Chapter 6. This book belongs to: Teacher:

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 information

Create 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?

Create 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 information

Algebra 1 Practice Test

Algebra 1 Practice Test Part 1: Directions: For questions 1-20, circle the correct answer on your answer sheet. 1. Solve for x: 2(x+ 7) 3(2x-4) = -18 A. x = 5 B. x = 11 C. x = -11 D. x = -5 2. Which system of equations is represented

More information

[ :~~ ~ ~?:~:::~ ~~~:~.i~~.:j Choose the correct answer.

[ :~~ ~ ~?:~:::~ ~~~:~.i~~.:j Choose the correct answer. [ :~~ ~ ~?:~:::~ ~~~:~.i~~.: Choose the correct answer.. What is the solution of this system of equations? y=- = 7-4y A. (5,3) B. (3,-5) C. (-3,-5) D. (-5,3). Solve the system of equations. y=+5 y- = 3

More information

Addition and Subtraction of real numbers (1.3 & 1.4)

Addition and Subtraction of real numbers (1.3 & 1.4) Math 051 lecture notes Professor Jason Samuels Addition and Subtraction of real numbers (1.3 & 1.4) ex) 3 + 5 = ex) 42 + 29 = ex) 12-4 = ex) 7-9 = ex) -3-4 = ex) 6 - (-2) = ** CHECK YOUR SIGNS ** IDENTIFY

More information

CRS SKILL LEVEL DESCRIPTION

CRS SKILL LEVEL DESCRIPTION GRE 501 LESSON/NOTES Period Name CRS SKILL LEVEL DESCRIPTION Level 1 ALL students must GRE 301 Locate points on the number line attain mastery at this level R- XEI 506 Solve first degree inequalities that

More information

3. Find the area for each question below. a. (3x 2)(2x + 5) b. 4. Simplify the expressions below. is equal to 1, what is the value of a?

3. Find the area for each question below. a. (3x 2)(2x + 5) b. 4. Simplify the expressions below. is equal to 1, what is the value of a? Permitted resources: 2018 2019 Algebra 1 Midterm Review FSA Approved calculator Algebra 1 FSA Reference Sheet 1. The expression 13x + 5 represents the number of marbles you have after shopping at the game

More information

Algebra I System of Linear Equations

Algebra I System of Linear Equations 1 Algebra I System of Linear Equations 2015-11-12 www.njctl.org 2 Table of Contents Click on the topic to go to that section Solving Systems by Graphing Solving Systems by Substitution Solving Systems

More information

Name Vetter Midterm REVIEW January 2019

Name Vetter Midterm REVIEW January 2019 Name Vetter Midterm REVIEW January 2019 1. Name the property that justifies each step in the following equation: 3x + 1+ 2x 7 = x + 22 ( 3x + 2x + 1 7 = x + 22 ( (2) x(3 + 2) 6 = x+ 22 5x 6 = x+ 22 (3)

More information

Elementary Algebra SAMPLE Final Examination Fall 2015

Elementary Algebra SAMPLE Final Examination Fall 2015 Elementary Algebra NAME: SAMPLE Final Examination Fall 2015 You will have 2 hours to complete this exam. You may use a calculator but must show all algebraic work in the space provided to receive full

More information

1.3 Solving Systems of Linear Equations: Gauss-Jordan Elimination and Matrices

1.3 Solving Systems of Linear Equations: Gauss-Jordan Elimination and Matrices 1.3 Solving Systems of Linear Equations: Gauss-Jordan Elimination and Matrices We can represent a system of linear equations using an augmented matrix. In general, a matrix is just a rectangular arrays

More information

Note: Two perpendicular lines form a system of the first type. (Nothing special about being )

Note: Two perpendicular lines form a system of the first type. (Nothing special about being ) Math 100 Elementary Algebra Sec 7.1: Solving Linear Systems by Graphing Two or more equations [inequalities] in several variables that are considered simultaneously are called a system of equations [inequalities].

More information

Algebra I. Systems of Linear Equations and Inequalities. 8th Grade Review. Slide 1 / 179 Slide 2 / 179. Slide 4 / 179. Slide 3 / 179.

Algebra 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 information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION COURSE I. Wednesday, August 16, :30 to 11:30 a.m.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION COURSE I. Wednesday, August 16, :30 to 11:30 a.m. The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE I Wednesday, August 16, 2000 8:30 to 11:30 a.m., only Notice... Scientific

More information