You isolate one variable. Let's say that x will be that variable in the first equation:
x-y=1
+y +y
x=y+1
So now you have the equation for x. All you have to do is substitute it into the other:
x=y+1
(y+1)+y=3
Combine like terms and solve:
2y+1=3
-1 -1
2y=2
2y/2=2/2
y=1
Now that you have the value of one, substitute it into either of the equations to find x.
If you put it in the first:
x-1=1
+1 +1
x=2
If you put it into the other, you would get the same answer.
Therefore, y=1 and x=2
