I'm having some trouble with this discrete math problem.
I'm given this equation: $7x + 9y \equiv 0 \bmod 31$ and $2x -5y \equiv 2 \bmod 31$
And I've solved like I did my other one (which turned out correct), coming to $14x+18y-14x+35y=-14\pmod{31} \implies 53y=-14\mod31=17\pmod{31}$.
My question: how do you go about solving $53y=17\mod31$? I know how to do this when the multiplier on the left is smaller, using extended Euclid's algorithm, which is all I've learned from my class so far (no Euler thing). I know the answer is 5, but how do I arrive at that? This one doesn't seem to work with extended Euclid's.