Решите систему уравнений 2x+y=4; xy+2x=-12.

Ответ:

\[\left\{ \begin{matrix} 2x + y = 4\ \ \ \ \ \ \ \ \ \\ xy + 2x = - 12 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} y = 4 - 2x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x(4 - 2x) + 2x = - 12 \\ \end{matrix} \right.\ \]

\[4x - 2x^{2} + 2x + 12 = 0\]

\[- 2x^{2} + 6x + 12 = 0\ \ \ \ |\ :( - 2)\]

\[x^{2} - 3x - 4 = 0\]

\[x_{1} + x_{2} = 3;\ \ x_{1} \cdot x_{2} = - 4\]

\[x_{1} = 4;\ \ \ \ x_{2} = - 1\]

\[\left\{ \begin{matrix} x = 4\ \ \ \\ y = - 4 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = - 1 \\ y = 6\ \ \ \\ \end{matrix} \right.\ \]

\[Ответ:(4;\ - 4);\ \ ( - 1;6).\]