4x - 5y = 3
8x + 15y = -24
multiply the top equation by 2 on both sides
8x - 10y = 6
8x + 15y = -24
add 10y to both sides in the top equation and subtract 15y from both sides in the bottom equation
8x = 6 + 10y
8x = -24 - 15y
see how the left sides of the equations are both 8x? the same? that means the right sides are the same too, so we can do this:
6 + 10y = -24 - 15y
25y + 6 = -24
25y = -30
y = -30/25
y = -6/5
4x - 5y = 3
4x - 5(-6/5) = 3
4x + 6 = 3
4x = -3
x = -3/4
Answer: x = -3/4, y = -6/5