Solving Systems of Equations:Solving Systems of Equations:The Elimination MethodThe Elimination Method

Solving Systems of Equations:Solving Systems of Equations:The Elimination MethodThe Elimination Method

Example 1

x – y = 7 x + y = 3

2x + 0y = 102x = 10

x = 5

x + y = 35 + y = 3

y = -2

(5,-2)

Solve using the elimination method.

REMEMBER:Always check yoursolution in the originalequations!

Example 2

2x + 3y = 11-2x + 9y = 10x + 12y = 12 12y =

12y = 1

2x + 3y = 112x + 3(1) =

112x + 3 = 11 2x = 8

x = 4

(4,1)

Solve using the elimination method.

Example 3Solve using the elimination method.

3x – y = 8x + 2y = 5x + 2y = 5

write in standard form

3x – y = 8multiply as needed(-3)( )

( )(-3)

3x – y = 8-3x – 6y = -

15addition property

-7y = -7 y = 1

3x - (1) = 8 3x = 9

x = 3

(3,1)

Example 4

8x 2y 10

4x 15 3y

4x – 3y = 15

write in standard form

8x + 2y = -10 multiply as needed(-2)( ) ( )(-2)

8x + 2y = -10-8x + 6y = -30 addition property

8y = -40y = -

5

8x + 2(-5) = -10 8x - 10 = -

10 8x = 0x = 0(0,-5)

Solve using the elimination method.

Practice

1)

Solve using the elimination method.

x y 5

2x y 4

2)

3x 3y 6

3x 3y 0

5x 3y 17

5x 2y 3

8x 11y 37

11y 7 2x

3) 4)

5) 2x + ⅔y = 4 x - ½y = 7