Решите систему уравнений: 3x^2+10xy+3y^2=0; x^2-xy-y^2=11.

\[x^{2} - x( - 3x) - ( - 3x)^{2} = 11\]

\[x^{2} + 3x^{2} - 9x^{2} = 11\]

\[- 5x^{2} = 11\]

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

\[( - 3y)^{2} - ( - 3y)y - y^{2} = 11\]

\[9y^{2} + 3y^{2} - y^{2} = 11\]

\[11y^{2} = 11\]

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

\[y_{1} = 1 \Longrightarrow \text{\ \ \ \ \ \ \ \ \ \ }\]

\[\Longrightarrow \ x_{1} = - 3 \cdot 1 = - 3.\]

\[y_{2} = - 1 \Longrightarrow \text{\ \ \ \ \ \ \ }\]

\[\Longrightarrow x_{2} = - 3 \cdot ( - 1) = 3.\]

\[Ответ:( - 3;1),\ (3;\ - 1).\]