Решите систему уравнений: y+4/x=-2; x-6/y=6.

\[x\left( - 2 - \frac{4}{x} \right) - 6 = 6 \bullet \left( - 2 - \frac{4}{x} \right)\]

\[- 2x - 4 - 6 = - 12 - \frac{24}{x}\]

\[\frac{24}{x} - 2x = - 2\ \ \ \ \ \ \ \ \ | \cdot x\]

\[24 - 2x^{2} = - 2x\]

\[2x^{2} - 2x - 24 = 0\ \ \ \ \ \ \ \ |\ :2\]

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

\[D = ( - 1)^{2} - 4 \cdot 1 \cdot ( - 12) =\]

\[= 1 + 48 = 49\]

\[x_{1} = \frac{4 + \sqrt{49}}{2} = \frac{1 + 7}{2} = \frac{8}{2} = 4\]

\[x_{2} = \frac{1 - \sqrt{49}}{2} = \frac{1 - 7}{2} = \frac{- 6}{2} =\]

\[= - 3\]

\[x_{1} = 4 \Longrightarrow \ \]

\[\Longrightarrow y_{1} = - 2 - \frac{4}{4} = - 2 - 1 = - 3.\]

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

\[\Longrightarrow y_{2} = - 2 - \frac{4}{- 3} = - 2 + 1\frac{1}{3} =\]

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

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