Let $(x_1,y_1),$ $(x_2,y_2),$ $\dots,$ $(x_n,y_n)$ be the real solutions to the system \begin{align*} x + 8y &= 7, \\ x^3 + 8y^3 &= 7. \end{align*}Enter $x_1 + y_1 + x_2 + y_2 + \dots + x_n + y_n.$
The only solution is (x,y) = (-1,1), so the answer is (-1) + 1 = 0.
