ERMAHGERD I JUST FOUND MY OLD NOTES ON IT
Say you have
3x -2y=1
+2x +2y=4 (you choose to eliminate one of the variables, in this case, the -2y, so you eliminate it by adding 2y, and then you have to add two across the equation. Granted, I don't know where the 4 came from that)
So now you have
5x=5
x=1
Then, you just check your answer! (By substituting the 1 for the x in the original equation)
2(1)+2y=4
2+2y=4
2y=2
y=1
Vwala!!!!