\[\left\{ \begin{matrix} 9x^{2} - 12xy + 4y^{2} = 9 \\ x + 2y = 9\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} x = 9 - 2y\ \ \ \ \ \ \ \ \\ (3x - 2y)^{2} = 9 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} x = 9 - 2y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \left( 3(9 - 2y) - 2y \right)^{2} = 9 \\ \end{matrix} \right.\ \]
\[(27 - 6y - 2y)^{2} = 9\]
\[(27 - 8y)^{2} = 9\]
\[27 - 8y = 3\ \ \ \ \ \ \ \ \ \ \ \ \ 27 - 8y = - 3\]
\[- 8y = - 24\ \ \ \ \ \ \ \ \ \ \ \ \ - 8y = - 30\]
\[y = 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ y = \frac{30}{8} = \frac{15}{4} = 3,75\]
\[\left\{ \begin{matrix} y = 3 \\ x = 3 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} y = 3,75 \\ x = 1,5\ \\ \end{matrix} \right.\ \]
\[Ответ:(3;3);\ \ (1,5;3,75).\]