Решите систему уравнений: y-5/x=-2; x+2/y=3.

\[x\left( \frac{5}{x} - 2 \right) + 2 = 3 \bullet \left( \frac{5}{x} - 2 \right)\]

\[- 5 - 2x + 2 = \frac{15}{x} - 6\]

\[2x + \frac{15}{x} - 6 - 7 = 0\]

\[2x - 13 + \frac{15}{x} = 0\ \ \ \ \ \ \ \ | \cdot x\]

\[2x^{2} - 13x + 15 = 0\]

\[D = ( - 13)^{2} + 4 \cdot 2 \cdot 15 =\]

\[= 169 - 120 = 49\]

\[x_{1} = \frac{13 + \sqrt{49}}{2 \cdot 2} = \frac{13 + 7}{4} = \frac{20}{4} =\]

\[= 5\]

\[x_{2} = \frac{13 - \sqrt{49}}{2 \cdot 2} = \frac{13 - 7}{4} = \frac{6}{4} =\]

\[= 1\frac{2}{4} = 1,5\]

\[x_{1} = 5 \Longrightarrow \ \ \ \ \ \ \ y_{1} = \frac{5}{5} - 2 =\]

\[= 1 - 2 = - 1.\]

\[x_{2} = 1,5 \Longrightarrow \ \ \ \ y_{2} = \frac{5}{1,5} - 2 =\]

\[= 3\frac{1}{3} - 2 = 1\frac{1}{3}.\]

\[Ответ:(5;\ - 1),\ \left( 1,5;1\frac{1}{3} \right).\]