Solution:

The given equations can be written as
$\begin{array}{l}
\frac{5}{x}+\frac{2}{y}=6\dots \dots (i) \\
\frac{-5}{x}+\frac{4}{y}=-3\dots \dots(ii)
\end{array}$
Adding equation(i) and equation(ii), we obtain
$\frac{6}{y}=3 \Rightarrow y=2$
Substituting $y=2$ in equation(i), we have
$\frac{5}{x}+\frac{2}{2}=6 \Rightarrow \mathrm{x}=1$
As a result, $x=1$ and $y=2$