Решите систему уравнений x+5y=-3; xy+11y=-36.

Ответ:

\[\left\{ \begin{matrix} x + 5y = - 3\ \ \ \ \ \ \\ xy + 11y = - 36 \\ \end{matrix} \right.\ \text{\ \ }\]

\[\left\{ \begin{matrix} x = - 5y - 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ ( - 5y - 3)y + 11y = - 36 \\ \end{matrix} \right.\ \]

\[- 5y^{2} - 3y + 11y + 36 = 0\ \ \ \]

\[- 5y^{2} + 8y + 36 = 0\ \ \ \ \ |\ :( - 1)\]

\[5y^{2} - 8y - 36 = 0\]

\[D = 16 + 180 = 196\]

\[y_{1} = \frac{4 + 14}{5} = \frac{18}{5} = 3,6\]

\[y_{2} = \frac{4 - 14}{5} = - \frac{10}{5} = - 2.\]

\[\left\{ \begin{matrix} y = 3,6\ \ \\ x = - 21 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} y = - 2 \\ x = 7\ \ \ \\ \end{matrix} \right.\ \]

\[Ответ:(7;\ - 2)\ и\ ( - 21;3,6)\]