Решите систему уравнений: x^2+xy=6; xy+y^2=3.

Ответ:

\[\left\{ \begin{matrix} x^{2} + xy = 6 \\ xy + y^{2} = 3 \\ \end{matrix}\text{\ \ \ \ \ \ \ } \right.\ \text{\ \ \ \ }\]

\[\left\{ \begin{matrix} x(x + y) = 6 \\ y(x + y) = 3 \\ \end{matrix}\text{\ \ \ \ \ \ } \right.\ \text{\ \ \ }\]

\[\left\{ \begin{matrix} \frac{x}{y} = 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ y(x + y) = 3 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x = 2y\ \ \\ 3y^{2} = 3 \\ \end{matrix}\text{\ \ \ \ \ \ \ \ \ } \right.\ \text{\ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = 2y \\ y^{2} = 1 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[\left\{ \begin{matrix} y = 1 \\ x = 2 \\ \end{matrix}\ \ \ \ \ \ или\ \ \right.\ \left\{ \begin{matrix} y = - 1 \\ x = - 2 \\ \end{matrix} \right.\ \]

\[Ответ:(2;1),\ ( - 2;\ - 1)\text{.\ }\]