Решебник по алгебре 8 класс Мерзляк Задание 134

\[\boxed{\text{134\ (134).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ \left\{ \begin{matrix} x + y = 8\ \ \ \ \ \\ 3x - 2y = 9 \\ \end{matrix}\text{\ \ \ \ \ \ \ \ \ } \right.\ \]

\[\left\{ \begin{matrix} x = 8 - y\ \ \ \ \ \\ 3x - 2y = 9 \\ \end{matrix}\ \right.\ \]

\[3 \cdot (8 - y) - 2y = 9\]

\[24 - 3y - 2y = 9\]

\[5y = 15\]

\[y = 3.\]

\[\left\{ \begin{matrix} x = 8 - y \\ y = 3\ \ \ \ \ \ \ \ \\ \end{matrix}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ }\ \right.\ \]

\[\left\{ \begin{matrix} x = 8 - 3 \\ y = 3\ \ \ \ \ \ \ \\ \end{matrix}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 5 \\ y = 3 \\ \end{matrix} \right.\ \right.\ \]

\[Ответ:x = 5;\ y = 3.\]

\[2)\ \left\{ \begin{matrix} 2x + 5y = 13\ \ \\ 3x - 5y = - 13 \\ \end{matrix} + \right.\ \]

\[5x = 0\]

\[x = 0\]

\[\left\{ \begin{matrix} x = 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 2x + 5y = 13 \\ \end{matrix}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ } \right.\ \]

\[\left\{ \begin{matrix} x = 0\ \ \ \ \ \\ 5y = 13 \\ \end{matrix}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 0\ \ \\ y = \frac{13}{5} \\ \end{matrix} \right.\ \right.\ \]

\[Ответ:x = 0;\ y = 2,6\text{.\ }\]