Решите систему уравнений: 5/x-6/y=2; 10/x-9/y=13.

\[\left\{ \begin{matrix}
\frac{5}{x} - \frac{6}{y} = 2\ \ \ \ \\
\frac{10}{x} - \frac{9}{y} = 13 \\
\end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[Пусть\ \ \frac{5}{x} = a;\ \ \frac{3}{y} = b:\]

\[\left\{ \begin{matrix}
a - 2b = 2\ \ \ \ \ \\
2a - 3b = 13 \\
\end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix}
a = 2b + 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\
2 \cdot (2b + 2) - 3b = 13 \\
\end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix}
a = 2b + 2\ \ \ \ \ \ \ \ \ \ \ \ \ \\
4b + 4 - 3b = 13 \\
\end{matrix} \right.\ \]

\[\left\{ \begin{matrix}
a = 2b + 2 \\
b = 9\ \ \ \ \ \ \ \ \ \ \\
\end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix}
b = 9\ \ \ \ \ \ \ \ \ \ \ \ \ \ \\
a = 2 \cdot 9 + 2 \\
\end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix}
b = 9\ \ \\
a = 20 \\
\end{matrix} \right.\ \]

\[Подставим:\]

\[\left\{ \begin{matrix}
\frac{5}{x} = 20\ \ \ | \cdot x \\
\frac{3}{y} = 9\ \ \ \ \ | \cdot y \\
\end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix}
5 = 20x \\
3 = 9y\ \ \ \\
\end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix}
x = \frac{5}{20} = \frac{1}{4} \\
y = \frac{3}{9} = \frac{1}{3}\text{\ \ } \\
\end{matrix} \right.\ \]

\[Ответ:\left( \frac{1}{4};\frac{1}{3} \right).\]