Решите систему уравнений 3x+y=-1; x-xy=8.

Ответ:

\[\left\{ \begin{matrix} 3x + y = - 1 \\ x - xy = 8\ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} y = - 1 - 3x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x - x( - 1 - 3x) = 8 \\ \end{matrix} \right.\ \]

\[x + x + 3x^{2} - 8 = 0\]

\[3x^{2} + 2x - 8 = 0\]

\[D = 1 + 24 = 25\]

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

\[x_{2} = \frac{- 1 - 5}{3} = - 2.\]

\[\left\{ \begin{matrix} x = 1\frac{1}{3} \\ y = - 5 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} x = - 2 \\ y = 5\ \ \ \\ \end{matrix} \right.\ \ \]

\[Ответ:\left( 1\frac{1}{3}; - 5 \right);\ \ ( - 2;5).\]