Section 7 – 3Solving Systems

UsingElimination

Objectives:To solve systems by adding or

subtractingTo multiply first when solving systems

Elimination Method:

Add or subtract equations to eliminate a variable.

REMEMBER: Opposites Cancel!

- 5 + 5 = 0 5x + -5x = 0

Example 1Adding/Subtracting

EquationsA) Solve using elimination. 5x – 6y = -32

3x + 6y = 48

B) Solve using elimination. 6x – 3y = 3-6x + 5y = 3

C) Solve using elimination. 2x – 3y = 612x + y = - 7

Homework Answers:

1) (6, -6) 2) (7, -1)

3) (10, -1) 4) (-1, -1)

5) (-1, 3)

WARM UPSolve using elimination. 2x + 18y = - 9

4x + 18y = -27

Section 7 – 3Continued

Objectives:To multiply first when solving

systems

Example 2 Multiplying One Equation

A) Solve by the elimination method.2x + 5y = - 2210x + 3y = 22

B) Solve by the elimination method.-2x + 15y = -327x – 5y = 17

C) Solve by the elimination method.-6x + 5y = 43x + 4y = 11

D) Solve by the elimination method.3x + 6y = -6-5x – 2y = -14

Section 7 – 3Continued

(Day 3)

Objectives:To multiply first when solving

systems

Example 3 Multiplying Both Equations

A) Solve by the elimination method.4x + 2y = 147x – 3y = - 8

B) Solve by the elimination method.15x + 3y = 910x + 7y = - 4

C) Solve by the elimination method.3x+ 5y = 105x + 7y = 10

D) Solve by the elimination method.7p + 5q = 28p – 9q = 17

Example 4 Word ProblemsA) Your community center sells a total of 292 tickets for a basketball game. An adult ticket costs $3. A student ticket costs $1. The sponsors collect $470 in ticket sales. Write and solve a system to find the number of each type of ticket sold.

B) The freshman class sells a total of 64 tickets to a play. A student ticket costs $1 and an adult ticket costs $2.50. Your class collects $109 in total ticket sales. How many adult tickets did you sell? How many student tickets did you sell?

C) Suppose the Junior Class sells gift wrap for $4 per package and greeting cards for $10 per package. Your class sells 205 packages in all and receives a total of $1084. Find the number of packages of gift wrap and the number of packages of greeting cards sold.

D) Suppose the band sells bags of popcorn for $5 per bag and bags of mixed nuts for $8 per bag. The band sells a total of 240 bags and receives a total of $1614. Find the number of bags of popcorn and the number of bags of mixed nuts sold.