7.4

5x + 2y = 16 5x + 2y = 16 3x – 4y = 20 3x – 4y = 20 In this linear system neither variable can be eliminated by adding the equations. 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. For systems like this you can multiply one or both equations by a constant so adding will result in elimination.

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 = 16 3x – 4y = 20 2( )10x + 4y = 32 3x – 4y = 20 13x = X = 4 3(4) – 4y = – 4y = 20 -4y = 8 Y = -2 (4,-2) 5x + 2y = 16 3x – 4y = 20

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 = 1 7x – 12y = 23 -4( ) 3( ) -8x + 36y = -4 21x - 36y = 69 13x = X = 5 2(5) – 9y = 1 10 – 9y = 1 -9y = -9 Y = 1 (5,1) 2x – 9y = 1 7x – 12y = 23

6x – 2y = 1 -2x + 3 = -5 2x + 5y = 3 3x + 10y = -3 3x – 7y = 5 9y = 5x + 5