ГДЗ по алгебре 7 класс Макарычев ФГОС Задание 1084

\[\boxed{\text{1084.}\text{\ }еуроки - ответы\ на\ пятёрку}\]

\[\textbf{а)}\ \left\{ \begin{matrix} y = x - 1\ \ \ \ \ \ \\ 5x + 2y = 16 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} y = x - 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 5x + 2 \cdot (x - 1) = 16 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} y = x - 1\ \ \ \ \ \ \ \ \ \ \ \ \ \\ 5x + 2x - 2 = 16 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} y = x - 1 \\ 7x = 18\ \ \ \\ \end{matrix} \right.\ \ \]

\[\left\{ \begin{matrix} x = \frac{18}{7} = 2\frac{4}{7} \\ y = \frac{18}{7} - 1\ \ \ \ \\ \end{matrix} \right.\ \ \]

\[\left\{ \begin{matrix} x = 2\frac{4}{7}\text{\ \ \ \ \ \ \ \ \ \ \ } \\ y = \frac{11}{7} = 1\frac{4}{7} \\ \end{matrix} \right.\ \]

\[Ответ:\left( 2\frac{4}{7};\ \ 1\frac{4}{7} \right).\]

\[\textbf{б)}\ \left\{ \begin{matrix} x = 2 - y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 3x - 2y - 11 = 0 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x = 2 - y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2) \\ 3 \cdot (2 - y) - 2y - 11 = 0\ \ \ \ (1) \\ \end{matrix} \right.\ \]

\[(1)\ 6 - 3y - 2y - 11 = 0\]

\[- 5y = 5\]

\[y = - 1\]

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

\[x = 3\]

\[Ответ:(3;\ - 1).\]