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

Ответ:

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

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

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

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

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

\[a = 2\]

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

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

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

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

\[Ответ:(2;8).\]