\[\left\{ \begin{matrix} 3x^{2} + 2y^{2} + \frac{6}{3x^{2} + 2y^{2} + 1} = 3 \\ 9x^{2} - 8y^{2} + 7x - 6y = 5\ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[3x^{2} + 2y^{2} + 1 + \frac{6}{3x^{2} + 2y^{2} + 1} =\]
\[= 4\]
\[t = 3x^{2} + 2y^{2} + 1\]
\[t + \frac{6}{t} = 4\ \ \ \ \ \ \ \ | \cdot t\]
\[t^{2} + 6 = 4t\]
\[t^{2} - 4t + 6 = 0\]
\[D = ( - 4)^{2} - 4 \cdot 1 \cdot 6 =\]
\[= 16 - 24 = - 8 < 0 \Longrightarrow\]
\[\Longrightarrow нет\ решений.\]
\[\Longrightarrow ч.т.д.\]