Решите систему уравнений: x^2+3xy+2y^2=0; x^2+xy-y^2=1.

\[( - 2y)^{2} + ( - 2y)y - y^{2} = 1\]

\[4y^{2} - 2y^{2} - y^{2} = 1\]

\[y^{2} = 1\]

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

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

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

\[( - y)^{2} + ( - y)y - y^{2} = 1\]

\[y^{2} - y^{2} - y^{2} = 1\]

\[- y^{2} = 1\]

\[y^{2} = - 1 \Longrightarrow \ нет\ решения.\]

\[Ответ:( - 2;1),\ \ \ (2;\ - 1).\]