7.3 Elimination Method

Using Addition and Subtraction

Elimination Method

The third method used to solve systems of equations.

Elimination Method

Example: Solvex 3y 7

3x 3y 9

- =

+ =

Soln: (4, -1)

x - 3y = 73x + 3y = 9(+)

4x = 16

x - 3y = 7

x = 4

(4)- 3y = 7 - 3y = 3 y = -1

Elimination Method

Example: Solve2x 3y 11

5x 3y 14

- =

- =

Soln: (1, -3)

2x - 3y = 11 5x - 3y = 14(-)

x = 1

2x - 3y = 11

-3x = -3

2(1)- 3y = 11 2 - 3y = 11 - 3y = 9

y = -3

Elimination

The sum of two numbers is 48, and their difference is 24. What are the numbers?x + y = 48x – y = 24(+)

2x = 72

(36) + y = 48

Soln: (36, 12)

x = 36

y = 12

Elimination

Three times one number added to another number is 18. Twice the first number minus the other number is 12. Find the numbers.

3x + y = 182x – y = 12(+)

5x = 30

3(6) + y = 18

Soln: (6, 0) x = 6

18 + y = 18 y = 0

CAUTION!!

BEFORE YOU BEGIN, equations must be lined up! (x’s on top of x’s, y’s on top of y’s, #’s on top of #’s and = sign on top of = sign.

Homework:

Pg p385: 13-33odd