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No problem. I did a ton of these things like three years ago, and along with abstract equations and trigonometric identities (substituting to prove relationships http://en.wikipedia.org/wiki/List_of_trigonometric_identities), they're the math problems I consider the most fun.
Bul you are right, but you used combinations and not substitution (at least my school taught your method as combination and there's another method called substitution where you take one equation and find the value, substitute it into the other and find what that is and substitute back into the oringal to find both answers.