x+y=-4
4x+5y=-18

y = -x - 4
5y = -4x - 18

-5(y = -x - 4)
5y = -4x - 18

-5y = 5x + 20
5y = -4x - 18

0 = x + 2
x = -2

y = -(-2) - 4
y = 2 - 4
y = -2

Final answer is (-2,-2)