ГДЗ по алгебре 7 класс Макарычев ФГОС Задание 1093

\[\boxed{\text{1093.}\text{\ }еуроки - ответы\ на\ пятёрку}\]

\[\textbf{а)}\ \left\{ \begin{matrix} \frac{x}{3} - \frac{y}{2} = - 4\ \ \ | \cdot 6 \\ \frac{x}{2} + \frac{y}{2} = - 2\ \ \ | \cdot 2 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 2x - 3y = - 24\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (1) \\ x + y = - 4 \rightarrow x = - 4 - y\ \ (2) \\ \end{matrix} \right.\ \]

\[(1)\ \ 2 \cdot ( - 4 - y) - 3y = - 24\]

\[- 8 - 2y - 3y = - 24\]

\[- 5y = - 16\]

\[y = 3,2\]

\[(2)\ x = - 4 - 3,2\]

\[x = - 7,2\]

\[Ответ:( - 7,2;\ \ 3,2).\]

\[\textbf{б)}\ \left\{ \begin{matrix} \frac{a}{6} - 2b = 6\ \ \ \ \ \ \ \ \ \\ - 3a + \frac{b}{2} = - 37 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} b = 2 \cdot (3a - 37)\ \ \ \ \ \ \ \ \ (2) \\ \frac{a}{6} - 4 \cdot (3a - 37) = 6\ \ (1) \\ \end{matrix} \right.\ \]

\[(1)\ \frac{a}{6} - 12a + 148 = 6\]

\[\frac{a - 72a}{6} = - 142\]

\[- 71a = - 852\]

\[a = 12\]

\[(2)\ \ b = 2 \cdot (3 \cdot 12 - 37)\]

\[b = - 2\]

\[Ответ:(12;\ - 2).\]

\[\textbf{в)}\ \left\{ \begin{matrix} \frac{2m}{5} + \frac{n}{3} = 1\ \ \ | \cdot 15 \\ \frac{m}{10} - \frac{7n}{6} = 4\ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 6m + 5n = 15 \rightarrow n = \frac{15 - 6m}{5}\ \ \ (1) \\ \frac{m}{10} - \frac{7n}{6} = 4\ \ \ \ | \cdot 30\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2) \\ \end{matrix} \right.\ \]

\[(2)\ \ 3m -\]

\[- 35 \cdot \left( \frac{15 - 6m}{5} \right) = 120\]

\[3m - 7 \cdot (15 - 6m) = 120\]

\[3m - 105 + 42m = 120\]

\[45m = 225\]

\[m = 5\]

\[(1)\ \ \ n = \frac{15 - 6 \cdot 5}{5}\]

\[n = \frac{15 - 30}{5} = - \frac{15}{5} = - 3\]

\[Ответ:(5;\ - 3).\]

\[\textbf{г)}\ \left\{ \begin{matrix} 7x - \frac{3y}{5} = - 4\ \ | \cdot 5 \\ x + \frac{2y}{5} = - 3\ \ \ \ | \cdot 5 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 35x - 3y = - 20 \rightarrow y = \frac{35x + 20}{3}\ \ \ \ (1) \\ 5x + 2y = - 15\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2) \\ \end{matrix} \right.\ \]

\[(2)\ \ 5x + 2 \cdot \frac{35x + 20}{3} =\]

\[= - 15\ \ \ | \cdot 3\]

\[15x + 2 \cdot (35x + 20) = - 45\]

\[15x + 70x + 40 = - 45\]

\[85x = - 85\]

\[x = - 1\]

\[(1)\ \ y = \frac{35 \cdot ( - 1) + 20}{3}\]

\[y = \frac{- 35 + 20}{3} = - \frac{15}{3} = - 5\]

\[Ответ:( - 1;\ - 5).\]