Решите систему уравнений: x^2+xy-y^2=4; 3x+y=10.

Ответ:

\[- 11x^{2} + 70x - 104 = 0\ \ \]

\[11x^{2} - 70x + 104 = 0\]

\[D = 1225 - 1144 = 81\]

\[x_{1} = \frac{35 + 9}{11} = 4;\ \ \ \]

\[x_{2} = \frac{35 - 9}{11} = \frac{26}{11}\]

\[\left\{ \begin{matrix} x = 4\ \ \ \\ y = - 2 \\ \end{matrix} \right.\ \ \ \ \ или\ \]

\[\text{\ \ \ }\left\{ \begin{matrix} x = \frac{26}{11} = 2\frac{2}{11} \\ y = \frac{32}{11} = 2\frac{10}{11} \\ \end{matrix} \right.\ \]

\[Ответ:(4; - 2);\ \ \left( 2\frac{2}{11};2\frac{10}{11} \right).\]