Approaching modular arithmetic problems

I'm a little stumbled on two questions.

How do I approach a problem like $x*41 \equiv 1 \pmod{99}$.

And given $2$ modulo, $7x+9y \equiv 0 \pmod{31}$ and $2x−5y \equiv 2 \pmod{31}$ (solve for $x$ only)?

When I solve for $x$ for the latter, I got a fraction as the answer and I'm not sure if I can have a fraction as an answer? I'm not sure how to approach the first problem either.