Using linear congruence to solve a further equation

Question

I'm having trouble in applying the two linear equations and solving the overall question in general.

The question is: x ≡ 7 (mod 9) and y ≡ 3 (mod 9) where x and y are integers. Find z where 0 ≤ z ≤ 8 and 92x + 2y^2 ≡ z (mod 9)

I believe the gcd(1,9) = 1 thus there's a solution but I don't know where to go from there.

Any help is appreciated.

Answer 1

$92x\equiv 2x \equiv 14\equiv 5 \pmod{9}$ $2y^2\equiv 2\cdot 9 \equiv 0 \pmod{9}$ So, the answer is $z=5$.