If you're new to elimination, you may want to check out the Elimination Level 1 lesson first for some simpler problems. This lesson shows how to "fix" one or both equations with multiplication to get a variable to cancel.
The goal with the elimination method is to get one of the variables to cancel out when you add the two equations together. In the Level 1 lesson, either the x's or the y's canceled when we added the equations.
For example, if you add the two equations below the x terms will cancel because you have a positive 3x and a negative 3x.
In the system above, the x's cancel and we're left with an equation that's pretty easy to solve for y. (Check out the Level 1 Elimination Lesson to see an example.) Unfortunately, this doesn't happen every time.
You might get a system that's a little more complicated. Take a look at the system below. If we add the two equations, we still have both variables left. This is a problem we'll have to fix.