B2. Find all pairs of real numbers $x$ and $y$ that solve the system of equations

$$
\begin{aligned}
\frac{3}{x-4 y}+\frac{2}{x+y-5} & =0 \\
\frac{2}{x^{2}-4 y^{2}}+\frac{1}{x^{2}+y^{2}-5} & =0
\end{aligned}
$$

## 61st Mathematical Competition for High School Students in Slovenia

Selection Competition, March 16, 2017

## Problems for 2nd Year

## Time for solving: 45 minutes.