What is x2+y2x^2+y^2?

Algebra Level 3

{x2=8x+yy2=x+8y\begin{cases} x^2 = 8x + y \\ y^2 = x + 8y\end{cases} If the above equation hold for real x,yx,y provided xyx \neq y, then determine the numerical value of x2+y2x^2 + y^2.

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