5x + 3y = -1
-2x + 5y = -12
multiply the first equation by 2, the second by 5, add:
10x + 6y = -2
-10x + 25y = -60
______________
31y = -62
y = -2
using the first equation:
5x + 3(-2) = -1
5x - 6 = -1
5x = 5
x = 1
check using eq(2):
-2(1) + 5(-2) = -12
-2 - 10 = -12
-12 = -12
x = 1, y = -2