I don't even ever recall him giving us a lesson on three variable equations.
To make up the deficiency, you might want to try studying some online lessons, such as this one. In general, though, you'll be using the same techniques for three-variable, three-equation systems as you did for the simpler case covered in class.
Warning: As you add more variables and equations, it becomes that much easier to make silly arithmetic errors. (At least, that's the biggest problem I have! *blush*) Do your work very clearly and carefully!