Can't say what the teacher is doing wrong, if anything. and is correct, and given error free arithmetic should be the result of any solution method: Substitution, Elimination, Gauss-Jordan Row Reduction, and/or Cramer's Rule. Which is the case; I checked.
The problem could be that the teacher has specified a way of presenting the solution. I.e. s/he may want the answer in ordered pair form or perhaps even in solution set form:
Then again, it wouldn't be the first time that a teacher, textbook, and/or answer key was wrong. Won't be the last time either.
My calculator said it, I believe it, that settles it