If $a\equiv 4\pmod {13}$, a is integer, Find c ($0 \leq c \leq 12$) so that $c\equiv 9a\pmod {13}$

Question

If $a\equiv 4\pmod {13}$, a is integer, Find c ($0 \leq c \leq 12$) so that $c\equiv 9a\pmod {13}$.

I translated these into the form of definition: 13 | a-4 and 13|c-9a, then I got stuck on it. I don't know how to solve a two variables congruence. How to solve it?

Answer 1

If $a \equiv 4 \bmod 13$, then $9a \equiv 36 \bmod 13$.

Congruence is symmetric and transitive...