Elimination Method Cont.

7.4

Oh no!5x + 2y = 16

3x – 4y = 20

In this linear system neither variable can be eliminated by adding the equations.

For systems like this you can multiply one or both equations by a constant so adding will result in elimination.

What to do.

Step P: Multiply one or both equations.

Step 1: Add the equations.

Step 2: Solve for variable.

Step 3: Substitute into either equation and solve for other variable.

5x + 2y = 163x – 4y = 20

2( )

10x + 4y = 32 3x – 4y = 2013x = 52

13x = 5213 13

X = 4

3(4) – 4y = 2012 – 4y = 20-4y = 8Y = -2

(4,-2)

5x + 2y = 163x – 4y = 20

Multiplying both

Step P: Multiply one or both equations.

Step 1: Add the equations.

Step 2: Solve for variable.

Step 3: Substitute into either equation and solve for other variable.

2x – 9y = 17x – 12y = 23

-4( ) 3( )

-8x + 36y = -421x - 36y = 6913x = 65

13x = 6513 13

X = 5

2(5) – 9y = 110 – 9y = 1-9y = -9Y = 1

(5,1)

2x – 9y = 17x – 12y = 23

Practice Problems

6x – 2y = 1-2x + 3 = -5

2x + 5y = 33x + 10y = -3

3x – 7y = 59y = 5x + 5