Решите систему уравнений: (2a+1)/7+(2b+2)/5=1/5; (3a-2)/2+(b+4)/4=4.

Ответ:

\[\left\{ \begin{matrix} \frac{2a + 1}{7} + \frac{2b + 2}{5} = \frac{1}{5}\ \ \ | \cdot 35 \\ \frac{3a - 2}{2} + \frac{b + 4}{4} = 4\ \ \ \ \ \ | \cdot 4\ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[\left\{ \begin{matrix} 5 \cdot (2a + 1) + 7 \cdot (2b + 2) = 7 \\ 2 \cdot (3a - 2) + b + 4 = 16\ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 10a + 5 + 14b + 14 = 7 \\ 6a - 4 + b + 4 = 16\ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[\left\{ \begin{matrix} 10a + 14b = - 12\ \ \ \ \ \ \ \ \ \\ 6a + b = 16\ \ \ \ | \cdot ( - 14) \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 10a + 14b = - 12\ \ \ \ \ \ \ \ \ (1) \\ - 84a - 14b = - 224\ \ \ (2) \\ \end{matrix} \right.\ \]

\[(1) + (2) \Longrightarrow - 74a = - 236\]

\[\left\{ \begin{matrix} - 74a = - 236 \\ 6a + b = 16\ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} a = \frac{118}{37} = 3\frac{7}{37} \\ b = 16 - 6a\ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} a = 3\frac{7}{37}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ b = 16 - 6 \cdot \frac{118}{37} \\ \end{matrix} \right.\ \text{\ \ \ \ }\]

\[\ \left\{ \begin{matrix} a = 3\frac{7}{37}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ b = - \frac{116}{37} = - 3\frac{5}{37} \\ \end{matrix} \right.\ \]

\[Ответ:\left( 3\frac{7}{37};\ - 3\frac{5}{37} \right).\]