\[\left\{ \begin{matrix} 2x^{2} + 3y^{2} + \frac{7}{2x^{2} + 3y^{2} + 1} = 4 \\ 5x^{2} - 6y^{2} + 7x - 8y = 9\ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[2x^{2} + 3y^{2} + 1 + \frac{7}{2x^{2} + 3y^{2} + 1} =\]
\[= 5\]
\[t = 2x^{2} + 3y^{2} + 1\]
\[t + \frac{7}{t} = 5\ \ \ \ \ \ | \cdot t\]
\[t^{2} + 7 = 5t\]
\[t^{2} - 5t + 7 = 0\]
\[D = ( - 5)^{2} - 4 \cdot 1 \cdot 7 =\]
\[= 25 - 28 = - 3 < 0 \Longrightarrow\]
\[\Longrightarrow нет\ решений.\]
\[\Longrightarrow ч.т.д.\]