Solve the following system of equations:

$$
\begin{gathered}
\frac{x}{a+b}+\frac{y}{a-b}=2 \\
\frac{x-y}{b}=\frac{x+y}{a}
\end{gathered}
$$
Our system of equations can also be written as:

$$
\begin{gathered}
x(a-b)+y(a+b)=2\left(a^{2}-b^{2}\right) \\
x(a-b)-y(a+b)=0
\end{gathered}
$$

thus

$$
\begin{gathered}
2 x(a-b)=2\left(a^{2}-b^{2}\right) \\
x=a+b \quad \text { and } \quad y=a-b
\end{gathered}
$$

(Anna Darvas, Budapest.)