Here is a simple example.

x 11 (mod 39)

x 7 (mod 22)

I would greatly appreciate it if someone could explain how to do this. I know first of all that 39a+22b=1. I believe you are supposed to use Euclid's Algorithm right? I know how to do Euclid's Algorithm I just don't understand how to use it to solve the problem I have shown above. Please explain as much as you can, big test coming up soon!