Math Olympiad | Nice Algebra Problem | How to Find the Value of x and y

[@wes9627]

Since x and y are integers, 1^2+8^2=65, but that doesn't hold for the first equation. However (±1)^2+(-8)^2=65 also satisfies the first equation.
Thus, x=±1 and y=-8 are solutions as are x=-8 and y=±1

[@RealQinnMalloryu4]

(4)+(4)+(6)+(3)=17 (2^2)+(2^2)+(3^3)+(3) (1^1)+(1^2)+(1^1)+(3) (2)+(3) (y ➖ 3x+2).(32)+(33)(1^2)+(1^3) (2)+(3) (y ➖ 3x+2).