2016/037) Solve the Diophantine below $12x + 25 y = 331$

Taking mod 25 we get
$12x \equiv 6 \pmod {25}$
we need to find inverse of $12\pmod {25}$
It can be done many ways , as we see that $12 * 2 = 24$ so multiply both sides by 2 to get
$24 x \equiv 12 \pmod {25}$
or $ x \equiv -12 \pmod {25}$ or  $ x \equiv 13 \pmod {25}$
so $x = 13$ is one of the values and putting $x = 13$ in given equation we get $y = 6$
so one solution $ x= 13,y = 6$ and as $12 * (-25) + 25 * 12 = 0$ we get generic solution
$ x = 13 - 25t, y= 6 + 12t$