5x + 3y = 4
-4x + 5y = -18
multiply the top equation by 4 and the bottom equation by -5
20x + 12y = 16
20x - 25y = 90
subtract 12y from both sides in the top equation and add 25y to both sides in the bottom equation
20x = 16 - 12y
20x = 90 + 25y
see how the left sides are the same in both equations? that means the right sides are also the same, so we can do this:
16 - 12y = 90 + 25y
16 - 37y = 90
-37y = 74
y = -2
-4x + 5y = -18
-4x + 5(-2) = -18
-4x - 10 = -18
-4x = -8
x = 2
Answer: x = 2, y = -2