Решите систему уравнений: x/y+y/x=2 1/2; 2x-3y=3.

\[\left\{ \begin{matrix} \frac{x}{y} + \frac{y}{x} = 2\frac{1}{2} \\ 2x - 3y = 3 \\ \end{matrix} \right.\ \]

\[Пусть\ \ \ \frac{x}{y} = t:\ \ \]

\[t + \frac{1}{t} - 2\frac{1}{2} = 0\ \ \ \ \ \ \ \ \ \ | \cdot \ t \neq 0\]

\[t^{2} - 2\frac{1}{2}t + 1 = 0\ \ \ \ \ \ | \cdot 2\]

\[2t^{2} - 5t + 2 = 0\ \]

\[D = 25 - 16 = 9\]

\[\ t = \frac{5 + 3}{4} = 2;\ \ t = \frac{5 - 3}{4} = \frac{1}{2}\]

\[Ответ:(6;3),\ ( - 0,75; - 1,5).\]