solve by using subsitution:

4x+y=2
3y+2x=-1

from the first:

y = 2-4x

plug into the 2nd
3(2-4x) + 2x = -1
6 - 12x + 2x = -1
-10x = -7
x = 7/10
then y = 2 - 4(7/10) = -4/5