Решите систему уравнений: x/y-y/x=15/4; 2x-5y=9.

\[\left\{ \begin{matrix} \frac{x}{y} - \frac{y}{x} = \frac{15}{4}\text{\ \ \ } \\ 2x - 5y = 9 \\ \end{matrix} \right.\ \ \]

\[Пусть\ \frac{x}{y} = t:\]

\[t - \frac{1}{t} = \frac{15}{4}\ \ \ \ | \cdot 4t\]

\[4t^{2} - 15t - 4 = 0\]

\[D = 225 + 64 = 289\]

\[t_{1} = \frac{15 + 17}{8} = 4,\ \ \]

\[t_{2} = \frac{15 - 17}{8} = - \frac{1}{4}\]

\[Ответ:\left( \frac{9}{22};\ - 1\frac{7}{11} \right);\ \ (12;3).\]