You may want to review solving equations for one variable in terms of another first.
For a system of linear equations, there are three possibilities. Either it has:
Actually getting the solution is rather complicated, so ideally your teacher explained it to you. That said, there are two ways to do it; here's one of them. You want to solve one of the equatinos for one variable. This solution probably won't be a number; it will probably have letters in it; that's okay. Just substitute it into all the other equations wherever you see the letter you solved for. Now the new equations have one fewer letter in them (since you just got rid of one of them) so we can keep going.
Here's an example. Suppose we had the system −a + b = −1, −a + 2b = 0. First we solve the first equation for a. We get a = b + 1. Now we substitute the answer into the other equation. This gives us −(b + 1) + 2b = 0. This is an equation that we can solve for b, getting b = 1. This tells us what a is, since a = b + 1, so a = 2.
The two things that can go wrong are that we might end up at some point with either a contradictino or an identity. If we end up with a contradiction, then the system we started with was inconsistent. If we end up with an identity, then the system we started with was dependent.