Решите систему уравнений: y+4/x=-2; x-4/y=3.

\[x\left( - 1 - \frac{4}{x} \right) - 4 = 3 \bullet \left( - 2 - \frac{4}{x} \right)\]

\[- 2x - 4 - 4 = - 6 - \frac{12}{x}\]

\[\frac{12}{x} - 2x = 2\ \ \ \ \ \ \ \ \ | \cdot x\]

\[12 - 2x^{2} = 2x\]

\[2x^{2} + 2x - 12 = 0\ \ \ \ \ |\ :2\]

\[x^{2} + x - 6 = 0\]

\[D = 1^{2} - 4 \cdot 1 \cdot ( - 6) = 1 + 24 =\]

\[= 25\]

\[x_{1} = \frac{- 1 + \sqrt{25}}{2} = \frac{- 1 + 5}{2} = \frac{4}{2} =\]

\[= 2\]

\[x_{2} = \frac{- 1 - \sqrt{25}}{2} = \frac{- 1 - 5}{2} =\]

\[= \frac{- 6}{2} = - 3\]

\[x_{1} = 2 \Longrightarrow \text{\ \ \ \ \ \ \ \ \ }y_{1} = - 2 - \frac{4}{2} =\]

\[= - 2 - 2 = - 4.\]

\[x_{2} = - 3 \Longrightarrow \text{\ \ \ \ \ }y_{2} = - 2 - \frac{4}{- 3} =\]

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

\[Ответ:\ \ (2;\ - 4),\ \ \ \left( - 3;\ - \frac{2}{3} \right).\]