Section 7 3 Solving Systems Using Elimination Objectives

Section 7 – 3 Solving Systems Using Elimination Objectives: To solve systems by adding or subtracting To multiply first when solving systems

Elimination Method: Add or subtract equations to eliminate a variable. REMEMBER: -5+5=0 Opposites Cancel! 5 x + -5 x = 0

Example 1 A) Adding/Subtracting Equations Solve using elimination. 5 x – 6 y = -32 3 x + 6 y = 48

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

C) Solve using elimination. 2 x – 3 y = 61 2 x + y = - 7

Homework Answers: 1) (6, -6) 2) (7, -1) 3) (10, -1) 4) (-1, -1) 5) (-1, 3)

WARM UP Solve using elimination. 2 x + 18 y = - 9 4 x + 18 y = -27

Section 7 – 3 Continued Objectives: To multiply first when solving systems

Example 2 Multiplying One Equation A) Solve by the elimination method. 2 x + 5 y = - 22 10 x + 3 y = 22

B) Solve by the elimination method. -2 x + 15 y = -32 7 x – 5 y = 17

C) Solve by the elimination method. -6 x + 5 y = 4 3 x + 4 y = 11

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

Section 7 – 3 Continued (Day 3) Objectives: To multiply first when solving systems

Example 3 Multiplying Both Equations A) Solve by the elimination method. 4 x + 2 y = 14 7 x – 3 y = - 8

B) Solve by the elimination method. 15 x + 3 y = 9 10 x + 7 y = - 4

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

D) Solve by the elimination method. 7 p + 5 q = 2 8 p – 9 q = 17

Example 4 Word Problems A) 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.