1. 6.3 Elimination with Multiplication!
Objective

2. Bell Work 1. 2. Can you find the smiling penguin?
Find two numbers whose sum is 58 and whose difference is 16
21, 37

3. Elimination using Multiplication #1
Consider the system
6x + 11y = -5
6x + 9y = -3

4. Elimination using Multiplication
Consider the system
6x + 11y = -5 +
6x + 9y = -3
12x + 20y = -8
When we add equations together,
nothing cancels out

5. Elimination using Multiplication
Consider the system
-1 ( )
6x + 11y = -5
6x + 9y = -3

6. Elimination using Multiplication
Consider the system
- 6x - 11y = 5 +
6x + 9y = -3

7. Elimination using Multiplication
Consider the system
6x + 11y = -5
6x + 9y = -3
Lets substitute y = -1
ANSWER: ( 1, -1 )

8. You Try
4x + y = 7 4x – 2y = -2
SOLUTION: (1, 3)

9. Elimination using Multiplication #2
Consider the system
x + 2y = 6
Multiply by -3 to eliminate the x term
3x + 3y = -6

10. Elimination using Multiplication
Consider the system
-3 ( )
x + 2y = 6
3x + 3y = -6

11. Elimination using Multiplication
Consider the system
-3x + -6y = -18 +
3x + 3y = -6

12. Elimination using Multiplication
Consider the system
x + 2y = 6
Substitute y = 8
3x + 3y = -6
x + 2(8) = 6
ANSWER: (-10 , 8)

13. Examples 1. 2. x + 2y = 5 x + 2y = 4 2x + 6y = 12 x - 4y = 16
ANS: (3, 1)
ANS: (8, -2)