4x + y = 20
5x - 2y = 12
multiply the top equation by -2
-8x - 2y = -40
5x - 2y = 12
add 40 to both sides in the top equation and subtract 12 from both sides in the bottom equation
-8x - 2y + 40 = 0
5x - 2y - 12 = 0
add 2y to both sides in both equations
-8x + 40 = 2y
5x - 12 = 2y
see how the equations are the same on the right (both are 2y)? that means the left sides are the same too, so we can do this:
-8x + 40 = 5x - 12
40 = 3x - 12
52 = 3x
x = 52/3
4x + y = 20
4(52/3) + y = 20
208/3 + y = 20
y = 20 - 208/3
y = 60/3 - 208/3
y = -148/3
Answer: x = 52/3, y = -148/3
strange- these problems are usually designed to have answers that are whole numbers.