ГДЗ по алгебре 7 класс Макарычев ФГОС Задание 1086

\[\boxed{\text{1086.}\text{\ }еуроки - ответы\ на\ пятёрку}\]

\[\textbf{а)}\ \left\{ \begin{matrix} 2x + y = 12\ \ \\ 7x - 2y = 31 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} y = 12 - 2x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2) \\ 7x - 2 \cdot (12 - 2x) = 31\ \ \ (1) \\ \end{matrix} \right.\ \]

\[(1)\ \ 7x - 24 + 4x = 31\]

\[11x = 55\]

\[x = 5\]

\[(2)\ y = 12 - 2 \cdot 5\]

\[y = 2\]

\[Ответ:(5;2).\]

\[\textbf{б)}\left\{ \begin{matrix} y - 2x = 4 \\ 7x - y = 1 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} y = 4 + 2x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2) \\ 7x - (4 + 2x) = 1\ \ \ \ \ (1) \\ \end{matrix} \right.\ \]

\[(1)\ 7x - 4 - 2x = 1\]

\[5x = 5\]

\[x = 1\]

\[(2)\ \ y = 4 + 2 \cdot 1\]

\[y = 6\]

\[Ответ:(1;6).\]

\[\textbf{в)}\left\{ \begin{matrix} 8y - x = 4\ \ \ \ \\ 2x - 21y = 2 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x = 8y - 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (1) \\ 2 \cdot (8y - 4) - 21y = 2\ \ (2) \\ \end{matrix} \right.\ \]

\[(2)\ \ 16y - 8 - 21y = 2\]

\[- 5y = 10\]

\[y = - 2\]

\[(1)\ x = 8 \cdot ( - 2) - 4\]

\[x = - 20\]

\[Ответ:( - 20;\ - 2).\]

\[\textbf{г)}\left\{ \begin{matrix} 2x = y + 0,5\ \ \ \\ 3x - 5y = 12 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} y = 2x - 0,5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2) \\ 3x - 5 \cdot (2x - 0,5) = 12\ \ \ (1) \\ \end{matrix} \right.\ \ \]

\[(1)\ 3x - 10x + 2,5 = 12\]

\[- 7x = 9,5\]

\[x = - 9\frac{1}{2} \cdot \frac{1}{7} = - \frac{19}{2} \cdot \frac{1}{7} = - \frac{19}{14}\]

\[(2)y = 2 \cdot \left( - \frac{19}{14} \right) - 0,5\]

\[y = - \frac{19}{7} - \frac{1}{2} = \frac{- 38 - 7}{14} = - \frac{45}{14}\]

\[Ответ:\left( - \frac{19}{14};\ - \frac{45}{14} \right).\]