Решите систему уравнений: x^2-y^2=24; x-2y=7.

Ответ:

\[4y^{2} + 28y + 49 - y^{2} - 24 = 0\]

\[3y^{2} + 28y + 25 = 0\]

\[D_{1} = 196 - 75 = 121\]

\[y_{1} = \frac{- 14 + 11}{3} = - 1;\ \ \]

\[y_{2} = \frac{- 14 - 11}{3} = - \frac{25}{3}.\]

\[\left\{ \begin{matrix} y = - 1 \\ x = 5\ \ \ \ \\ \end{matrix} \right.\ \ \ \ \ \ \ или\ \ \ \ \left\{ \begin{matrix} y = - \frac{25}{3} \\ x = - \frac{29}{3} \\ \end{matrix} \right.\ \]

\[Ответ:(5; - 1);\ \ \left( - \frac{29}{3};\ - \frac{25}{3} \right).\]