Решите систему уравнений: 2x^2+3xy+y^2=0; x^2-xy-y^2=4.

\[1)\ \left\{ \begin{matrix} x + y = 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x^{2} - xy - y^{2} = 4\ \\ \end{matrix} \right.\ \ \ \ \ \ x = - y\]

\[( - y)^{2} - ( - y)y - y^{2} = 4\]

\[y^{2} + y^{2} - y^{2} = 4\]

\[y^{2} = 4\]

\[y_{1} = 2;\ \ \ y_{2} = - 2.\]

\[y_{1} = 2 \Longrightarrow x_{1} = - 2.\]

\[y_{2} = - 2 \Longrightarrow x_{2} = - ( - 2) = 2.\]

\[2)\ \left\{ \begin{matrix} 2x + y = 0\ \ \ \ \ \ \ \ \ \ \ \\ x^{2} - xy - y^{2} = 4 \\ \end{matrix} \right.\ \ \ \ \ \ \ y = - 2x\]

\[x^{2} - x( - 2x) - ( - 2x)^{2} = 4\]

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

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

\[x^{2} = - 4 \Longrightarrow \ \ \ \ нет\ решения.\]

\[Ответ:( - 2;2),\ \ \ (2;\ - 2).\]