Ok what you have to do is get one variable in the two equations equal but opposite to each other. You already have that in y in the first one and -y in the second. Sometimes you would have to do some manipulation to get there.
Next, add the two together:
4x+y=-5
+ 2x-y=-1
---—--------
6x=-6
x-1
Now plug in the -1 for x in one of the formulas above:
4(-1)+y=-5 solve for y
-4+y=-5
y=-5+4
y=-1
