Решите систему уравнений 2x^2-5y=27; 2x-y=7.

Ответ:

\[\left\{ \begin{matrix} 2x^{2} - 5y = 27 \\ 2x - y = 7\ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} y = 2x - 7\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 2x^{2} - 5(2x - 7) = 27 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[2x^{2} - 10x + 35 - 27 = 0\]

\[2x^{2} - 10x + 8 = 0\ \ \ \ \ \ |\ :2\]

\[x^{2} - 5x + 4 = 0\]

\[x_{1} + x_{2} = 5;\ \ \ x_{1} \cdot x_{2} = 4\]

\[x_{1} = 4;\ \ \ x_{2} = 1\]

\[\ \left\{ \begin{matrix} x = 4 \\ y = 1 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} x = 1\ \ \ \\ y = - 5 \\ \end{matrix} \right.\ \]

\[Ответ:(4;1)\ и\ (1;\ - 5).\]