TR-MO-R1 2010 Problem 3

$\begin{aligned} x^2 + 2y &= 2xy \\ x^3 + x^2y &= y^2 \end{aligned}$

denklem sistemini sağlayan kaç $(x, y)$ gerçel sayı ikilisi vardır?

a) 3 b) 2 c) 1 d) 0 e) Hiçbiri

Official text Turkish Mathematical Olympiad, first round 2010 official paper, page 2. Quoted with source.

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