Given that $a,b$ are integers and $a\equiv 4 \mod 13$ and $b\equiv 9 \mod 13$, find $c$ where $c\equiv 2a+3b\mod 13$

Question

$a\equiv 4 \mod 13 \\ b\equiv 9 \mod 13$

How do I find $c$ where $c\equiv 2a+3b\mod 13$?

I thought maybe $[(2\times4)+(3\times9)] \mod 13 = 9$ but I don't know if this is right.

Answer 1

from $$a\equiv 4\mod 13$$ and $$b\equiv 9\mod 13$$ we get $$2a+3b\equiv 27+8=35\equiv 9\mod 13$$