Warm-up-12/13/12Create the equation of the

line for each of the following tables.

1) 2) x y0 21 62 183 54

x y0 -51 32 113 19

xy 2(3) y 8x 5

Unit 2: Solving Systems of Equations

Key Ideas Properties of Equality Solving Systems of Equations

by Graphing by Substitution by Elimination

Word Problems Graphing Systems of Linear

Inequalities More Word Problems

Properties to know-WS 2.1• Addition Property of Equality

• Subtraction Property of Equality• Multiplication Property of Equality• Division Property of Equality• Reflexive Property of Equality• Symmetric Property of Equality• Transitive Property of Equality• Commutative Property of Addition and

Multiplication• Associative Property of Addition and Multiplication• Distributive Property• Identity Property of Addition and Multiplication• Multiplicative Property of Zero• Additive and Multiplicative Inverses

Example 1

Solve the equation a list the property 8(x + 2) = 2(y + 4) for y.

y 4x 4

Example 2Karla wants to save up for a prom dress.

She figures she can save $9 each week from the money she earns babysitting.

If she plans to spend up to $150 for the dress, how many weeks will it take her to save enough money?

17weeks

Example 3

• Use Graphing to solve the linear system.

2 7

3 6 12

y x

x y

(2,3)

-6 -4 -2 2 4 6

-6

-4

-2

2

4

6

Example 4

• Use substitution to solve the linear system.

2 2

6 2 16

y x

x y

(2,2)

Example 5

• Use elimination to solve the linear system.3 3 9

6 2 2

x y

x y

(1, 2)

Example 6

• Solve the linear system using any method.

3 5

5 3 7

x y

x y

(2,1)

Example 7

• Solve the linear system using any method.

( 1,3)

4 11

2 2 8

x y

x y

Example 8

• Solve the linear system using any method.6 9 18

2 3 10

x y

x y

(No Solution)

Example 9• You are selling tickets for a basketball

game. Student tickets cost $3 and general admission tickets cost $5. You sell 350 tickets and collect $1450.

• Use a system of linear equations to determine how many student tickets you sold?Student : x

General:y

x y 350

3x 5y 1450

150 student, 200 general admission

2

2

y x

x

Example 10

Graph

Example 11

Which equation corresponds to the graph shown?A. y = x + 1B. y = 2x + 1C. y = x – 2D. y = -3x – 2

Example 12Which graph would represent a system of linear equations that has no common coordinate pairs?

A B

C D

CW/HW

Mid-Term Unit #2 Review