\[\left\{ \begin{matrix} 2x^{2} + y^{2} + \frac{5}{2x^{2} + y^{2} + 1} = 2 \\ x^{2} - y^{2} + 5x - 7y = 11\ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[2x^{2} + y^{2} + 1 + \frac{5}{2x^{2} + y^{2} + 1} =\]
\[= 3\]
\[t = 2x^{2} + y^{2} + 1\]
\[t + \frac{5}{t} = 3\ \ \ \ \ \ \ \ \ | \cdot t\]
\[t^{2} + 5 = 3t\]
\[t^{2} - 3t + 5 = 0\]
\[D = ( - {3)}^{2} - 4 \cdot 1 \cdot 5 = 9 - 20 =\]
\[= - 11 < 0 \Longrightarrow нет\ \ решений.\]
\[\Longrightarrow ч.т.д.\]