Ch 5.4

Elimination (multiplication)

Objective:

To solve a system of linear equations using multi-step elimination

(multiplication and addition).

1) Rearrange the equations so that “like” terms are lined up.

2) Multiply one of the equations so OPPOSITES exist for one of the variables.

3) Add the two equations to each other to eliminate that variable.

4) Solve for the remaining variable.

5) Plug in the solution from Step 4 into either equation to solve for the other variable.

Rules

Check Your Answers!Plug in the x and y solutions into BOTH equations to

verify that they both make TRUE statements.

Solve using elimination

2x + 3y = 3 x + 6y = -3

Example 1

Multiply by (-2)

2x + 3y = 3

-2x - 12y = 6

-9y = 9

-9 -9y = -1

2x + 3y = 32x + 3(-1) = 3

+32x = 6

x = 3x = 3, y = -1

+

−3

-2( x + 6y = -3)

2x + 3y = 3

Solve using elimination

2x + 3y = -4 x – 4y = 9

Example 2

Multiply by (-2) 2x + 3y = -4

2x + 3y = - 4

11y = -22

11 11y = -2

2x + 3y = -42x + 3(-2) = -4

+62x = 2

x = 1x = 1, y = -2

+

-2( x – 4y = 9)

-2x + 8y = -18

−6

Solve using elimination

-4x − y = -12 8x − 4y = 0

Example 3

Multiply by (+2)

8x − 4y = 0

-8x − 2y = -24

-6y = -24

-6 -6y = 4

-4x − y = -12-4x − (4) = -12

-4x = -8

x = 2x = 2, y = 4

+

2(-4x – y = -12)

8x − 4y = 0

+4 4

Solve using elimination

2x +14y = -8 -6x + 7y = 24

Example 4

Multiply by (+3)

-6x + 7y = 24

6x + 42y = -24

49y = 0

49 49y = 0

2x + 14y = -82x + 14(0) = -8

2x = -8

x = -4x = -4, y = 0

+

3(2x + 14y = -8)

-6x + 7y = 24

0

Classwork

4x + 5y = -222x + y = -26

1) -x + 2y = 20 5x + y = 10

2)

-4x + 6y = 10-2x + 4y = 14

3) -2x – 5y = -16 -x + y = 13

4)

Classwork

-4x + 3y = 15x – 6y = 12

5) 2x + 8y = -8 -x − 10y = 16

6)

Classwork