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Question 296·Hard·Advanced Math

The ordered pair (x,y)(x, y) satisfies the system of equations

{x2−y=1y2−x=7\begin{cases} x^2 - y = 1 \\ y^2 - x = 7 \end{cases}

The system has exactly two real solutions. What is the greater of the two possible values of x+yx + y?