Решите систему уравнений: xy+x^2=30; xy+y^2=-5.

Ответ:

\[\left\{ \begin{matrix} xy + x^{2} = 30\ \\ xy + y^{2} = - 5 \\ \end{matrix}\text{\ \ \ } \right.\ ( + )\text{\ \ }\]

\[1.\ \left\{ \begin{matrix} x + y = 5\ \ \ \ \ \ \ \ \ \ \\ y(x + y) = - 5 \\ \end{matrix}\text{\ \ \ \ } \right.\ \]

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

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

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

\[2.\ \left\{ \begin{matrix} x + y = - 5\ \ \ \ \ \ \\ y(x + y) = - 5 \\ \end{matrix}\text{\ \ \ \ \ } \right.\ \]

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

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

\[Ответ:(6;\ - 1);\ \ ( - 6;1).\]