2000 Cayley Problem 25

For the system of equations x^2 + x^2y^2 + x^2y^4 = 525 and x + xy + xy^2 = 35, the sum of the real y values that satisfy the equations is

\textbf{(A)}\ 20\quad \textbf{(B)}\ 2\quad \textbf{(C)}\ \frac{3}{2}\quad \textbf{(D)}\ \frac{55}{2}\quad \textbf{(E)}\ \frac{5}{2}

If there are no answer choices shown, enter a numerical answer.

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