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MathNet 2008-part-04 — 165 problems (EN–VI) Question 23

Math Olympiad Vault · MathNet 2008-part-04 — 165 problems (EN–VI)

Question 23

Find all real numbers $x$ and $y$ that satisfy the equations
$$
\begin{aligned}
x^{3}+8 y^{3} & =x+2 y \\
2 x^{2} y+4 x y^{2} & =x+2 y
\end{aligned}
$$