Algebra

[Pages:54]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 equations in two variables by graphing Pgs: 1 ? 5 HW: Pgs: 6 ? 8

Chapter 6-2: SWBAT: solve systems of linear equations in two variables by substitution Pgs: 9 - 14 HW: Pgs: 15 ? 17

Lesson 6-3: SWBAT: solve systems of linear equations in two variables by elimination Pgs: 18 - 22 HW: Pgs: 23 ? 24

Word Problems: SWBAT: Write and solve word problems whose solution requires solving systems of linear equations in two variables Pgs: 25 - 30 HW: Pgs: 31 ? 33

Review Lesson 6-1 to 6-3: SWBAT: Demonstrate their knowledge of solving systems of linear equations in two variables Pgs: 34 - 38

Lesson 6-5: SWBAT: graph and solve linear inequalities in two variables Pgs: 39 ? 43 HW: Pgs: 44 ? 45

Lesson 6-6: SWBAT: graph and solve systems of linear inequalities in two variables Pgs: 46 - 49 HW: Pgs: 50 ? 52

Review

CHAPTER 6 EXAM

Chapter 6 ? 1 Solving Systems by Graphing

SWBAT: Identify solutions of systems of linear equations in two variables; Solve systems of linear equations in two variables by graphing Warm Up Midterm Review #1 ? See attached Sheet If two or more equation are given, we call this a system of equations. The solution to a system of

equations consists of the set of all ordered pairs, x, y, that satisfy (make true) all of the equations in the

system. In today's lesson, we will investigate ways of finding this solution set for two linear equations.

Practice: Use the graph below to estimate a solution to the system. Then check your solution algebraically. Solution: ( ___ , ___ ) Check

1

Practice: Identifying Solutions of Systems

Tell whether the ordered pair is a solution of the given system.

A)

(4, 1);

x 2y 6 x y 3

B)

(?1, 2);

2x 5y 8 3x 2y 5

x2y 6

x y 3

2x 5y 8

3x 2y 5

Example 2: Solving Systems of Linear Equations by Graphing All solutions of a linear equation are on its graph. To find a solution of a system of linear equations, you need a point that each line has in common. In other words, you need their point of intersection.

Directions: Solve each system by graphing. Check your answer. C)

Check:

D)

Check: 2

Practice: Solving Systems of Linear Equations by Graphing Directions: Solve each system by graphing. Check your answer.

3

4

Challenge / Regents Problem:

Summary: Exit Ticket:

y = 3x + 1 y = -x + 5

5

Chapter 6- 1 Solving Systems by Graphing HW

Tell whether the ordered pair is a solution of the given system.

x 3y 6 1) (3, 1); 4x 5y 7

3x 2y 14 2) (6, ?2); 5x y 32

x 3y 6

4x 5y 7

3x 2y 14

5x y 32

Solve each system by graphing. Check your answers.

3)

y x6

y

2x

9

Solution: __________

y x 6 4) y 3x 6

Solution: _________

Check:

Check: 6

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