Prove that $ a + 2b equiv 0 $ (mod 3) if and only if $ a equiv b $ (mod 3).

I need to prove it $ a + 2b equiv 0 $ (mod 3) if and only if $ a equiv b $ (mod 3).
I know you have to show both cases, but my teacher said that we were not supposed to use one to solve the other, so I'm stuck.