3x + y = -2
5x + 2y = -5
I'm choosing to eliminate y from both equations by multiplying the top equation by -2 and then adding down the columns.
-2[3x + y = -2] ---> -6x - 2y = 4
5x + 2y = -5
---> -x = -1 ---> x = 1
Replacing x with 1 in the top equation: 3(1) + y = -2
3 + y = -2
y = -5