Most of the time they aren't set up that nicely. You'll usually have to do a little dinking before something will drop out.
Look at this one:

If we just add straight down, nothing's going to drop out and we'll just get a mess.
But, check out the y guys:

If we could make this a  +4y,
the y's would drop out...
So, let's do it! Remember that we can multiply an equation by a number... So, let's multiply the second equation by a -2:
|  Remember to hit each guy! |  | 
Now, stick the x guy into either of the original equations. I'm going to go for the first one:

| The answer is (-1, |  | ) | 
Check it - and don't let that fraction freak you... These things happen!
YOUR TURN:
Solve by elimination:

* Hint: ditch the x!