\section*{Problem 5 - 071225}

All ordered pairs of real numbers \((x, y)\) are to be determined for which the system of equations

\[
\begin{aligned}
x \cdot\left(a x^{2}+b y^{2}-a\right) & =0 \\
y \cdot\left(a x^{2}+b y^{2}-b\right) & =0
\end{aligned}
\]

is satisfied. Here, \(a\) and \(b\) are real numbers with \(a \neq 0, b \neq 0\) and \(a \neq b\).