Решите систему уравнений: 2a/3+5b/12=7/6; 2a/5=4/5-3b/10.

Ответ:

\[\left\{ \begin{matrix} \frac{2a}{3} + \frac{5b}{12} = \frac{7}{6}\ \ \ \ | \cdot 12 \\ \frac{2a}{5} = \frac{4}{5} - \frac{3b}{10}\ \ \ \ | \cdot 10 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[\left\{ \begin{matrix} 4 \cdot 2a + 5b = 2 \cdot 7 \\ 2 \cdot 2a = 2 \cdot 4 - 3b \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 8a + 5b = 14\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 4a + 3b = 8\ \ \ | \cdot ( - 2) \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 8a + 5b = 14\ \ \ \ \ \ \ \ \ \ (1) \\ - 8a - 6b = - 16\ \ \ (2) \\ \end{matrix} \right.\ \]

\[(1) + (2) \Longrightarrow - b = - 2 \Longrightarrow b = 2\]

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

\[\left\{ \begin{matrix} b = 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 4a = 8 - 3b \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

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

\[\left\{ \begin{matrix} b = 2\ \ \ \\ a = 0,5 \\ \end{matrix} \right.\ \]

\[Ответ:(0,5;2).\]