1. Find all positive integer pairs $(x, y)$ that satisfy the equation
$$
2 x^{2}+5 y^{2}=11(x y-11)
$$
```
By rearranging and factoring, we get
\[
\begin{array}{l}
(2 x-y)(x-5 y)=-121 . \\
\text { The solution is }(x, y)=(14,27) .
\end{array}
\]
```