Use the method of "linear combinations":
-4x - 15y = 17
4x - 20y = 52
Add down the columns to get:
-35y = 69
y = 69/-35
Substitute this value back into either one of the original equations; I'll use the second one:
4x - 20(69/-35) = 52
4x = 88/7
x = 22/7
