-4x+y=6
-5x-y=21
Solve for one side of either equation. I will use the first equation and solve for y.
-4x+y=6
+4x +4x
Y=4x+6
-5x-y=21
Now when you substitute, make sure to distribute properly including the easily missed negative.
-5x-(4x+6)=21
-5x-4x-6=21
-9x-6=21
-9x=27
X=27/-9
X=-3
Now that you know X, substitute to find Y.
Y=4(-3)+6
Y=-12+6
Y=-6
So your final answer is:
X=-3 Y=-6
(-3,-6)