\[\left\{ \begin{matrix} x^{2} - 2xy - 3y^{2} = 0 \\ x^{2} + 2y^{2} = 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \ ( + )\]
\[\left( x^{2} + 2xy + y^{2} \right) - 4y^{2} = 0\]
\[(x + y)^{2} - (2y)^{2} = 0\]
\[(x + y - 2y)(x + y + 2y) = 0\]
\[(x - y)(x + 3y) = 0\]
\[x = y;\ \ \ x = - 3y:\]
\[1)\ x = y:\]
\[y^{2} + 2y^{2} = 3\]
\[3y^{2} = 3\]
\[y^{2} = 1\]
\[y = \pm 1\]
\[\left\{ \begin{matrix} y = 1 \\ x = 1 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = - 1 \\ y = - 1 \\ \end{matrix} \right.\ \]
\[2)\ x = - 3y:\]
\[( - 3y)^{2} + 2y^{2} = 3\]
\[9y^{2} + 2y^{2} = 3\]
\[11y^{2} = 3\]
\[y^{2} = \frac{3}{11}\]
\[y = \pm \frac{\sqrt{3}}{\sqrt{11}} = \pm \frac{\sqrt{33}}{11}\]
\[\left\{ \begin{matrix} y = \frac{\sqrt{33}}{11}\text{\ \ \ \ \ \ \ } \\ x = - \frac{3\sqrt{33}}{11} \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\left\{ \begin{matrix} y = - \frac{\sqrt{33}}{11} \\ x = \frac{3\sqrt{33}}{11}\text{\ \ } \\ \end{matrix} \right.\ \]
\(Ответ:( - 1;\ - 1);(1;1);\)
\[\left( - \frac{3\sqrt{33}}{11};\frac{\sqrt{33}}{11} \right);\left( \frac{3\sqrt{33}}{11};\ - \frac{\sqrt{33}}{11} \right).\]