There are two ways to do this. This example is nice to just add the two equations (you could also subtract for similar problems)
-4x+y=6
+
-5x-y=21
-----------
-9x+0=27
---> x=-3
Then plug into one of the equations and solve for y
-4*(-3)+y=6
= 12+y=6
--> y=(-6)
You should then check the other equation is true
--> -5*(-3)-(-6)=21
= 15+6=21 which is true.
Alternatively you can simply solve for y in terms of x in the first equation ---> y=6+4x
then substitute this equation for y into the second equation where ever you see y (be careful with the negative signs), solve for x, and use that result to find y. I recommend doing it both ways to make sure you don't make any mistakes.
Hope this helps!