Help with finding $x,y \in \mathbb{Z} $ such that work for statement with reminders

Question

So I have an expression $18x+14y$ and I have to find such $x,y \in \mathbb{Z} $ that expression $18x+14y$ , when divided by 63, will have a reminder 5.

So I know that I have to solve this equation:

$$18x+14y\equiv 5 (mod63)$$

But I don't know how to approach this kind of equation. Any help would be appreciated.

Answer 1

As the greatest common divisor of $18$ and $14$ is $2$, you can use the extended Euclidean algorithm to find $x', y'$ such that $$18x'+14y'=2.$$

Then, multiply the euation by $34$ and see what you get.