Решите систему уравнений: 3a/4+3b/8=9/2; 2a/3=b/12+2/3.

\[\left\{ \begin{matrix}
\frac{3a}{4} + \frac{3b}{8} = \frac{9}{2}\ \ \ \ \ | \cdot 8\ \\
\frac{2a}{3} = \frac{b}{12} + \frac{2}{3}\ \ \ \ | \cdot 12 \\
\end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix}
2 \cdot 3a + 3b = 4 \cdot 9 \\
4 \cdot 2a = b + 4 \cdot 2\ \ \ \\
\end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[\left\{ \begin{matrix}
6a + 3b = 36\ \ |\ :3 \\
8a - b = 8\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\
\end{matrix} \right.\ \]

\[\left\{ \begin{matrix}
2a + b = 12\ \ \ (1) \\
8a - b = 8\ \ \ \ \ (2) \\
\end{matrix} \right.\ \]

\[(1) + (2) \Longrightarrow 10a = 20\]

\[a = 2\]

\[\left\{ \begin{matrix}
a = 2\ \ \ \ \ \ \ \ \ \ \ \ \ \\
2a + b = 12 \\
\end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix}
a = 2\ \ \ \ \ \ \ \ \ \ \ \ \\
b = 12 - 2a \\
\end{matrix} \right.\ \text{\ \ \ \ }\]

\[\left\{ \begin{matrix}
a = 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\
b = 12 - 2 \cdot 2 \\
\end{matrix} \right.\ \text{\ \ \ \ }\]

\[\left\{ \begin{matrix}
a = 2 \\
b = 8 \\
\end{matrix} \right.\ \]

\[Ответ:(2;8).\]