Solve system by eliminating

Question

2x-4y=-4

3x+2y=22

Answer 1

2x-4y=-4

3x+2y=22

If we multiply the entire 2nd equation by 2, we should be able to eliminate the y variable. Like this;

2x - 4y = -4

2(3x + 2y = 22)

2x - 4y = -4

6x + 4y = 44

Now add the 2 equations (add the like terms) together.

2x + 6x = 8x; -4y + 4y = 0 (we eliminated the "y" terms); and -4 + 44 = 40. We are left with:

8x = 40

÷ 8 ÷ 8

x = 5

Now, plug the value for x into the 1st equation:

2(5) -4y = -4

10 - 4y = -4

-10 -10

-4y = -14

÷ -4 ÷ -4

y = 3.5

Let's check our answer:

2(5) - 4(3.5) = -4

6(5) + 4(3.5) = 44

10 - 14 = -4

30 + 14 = 44

-4 = -4

44 = 44

Answer 2

multiply 2nd by 2, then add to the 1st to eliminate y

6x + 4y = 44

2x -4y =-4

8x = 40

x = 5

2y = 22-3x = 22-15 = 7

y = 7/2