Решебник по алгебре 9 класс Мерзляк Задание 162

\[\boxed{\text{162\ (162).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ ax > - 1 - 7x\]

\[ax + 7x > - 1\]

\[x(a + 7) > - 1\]

\[a + 7 = 0\]

\[a = - 7\]

\[Ответ:\ неравенство\ имеет\ \]

\[множество\ решений\ \]

\[при\ a = - 7.\]

\[2)\ \left( a^{2} - 16 \right) \cdot x \geq a + 4\]

\[(a - 4)(a + 4) \cdot x \geq a + 4\]

\[a + 4 = 0\]

\[a = - 4\]

\[Ответ:неравенство\ имеет\ \]

\[множество\ решений\ \]

\[при\ a = - 4.\]

\[\boxed{\text{162.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ \left\{ \begin{matrix} 2x + y = 10\ \ | \cdot 2 \\ 4x - 7y = 2\ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 4x + 2y = 20 \\ 4x - 7y = 2\ \ \\ \end{matrix} \right.\ \ \ \ \ -\]

\[\left\{ \begin{matrix} 9y = 18\ \ \ \ \ \ \ \ \\ 4x - 7y = 2 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\left\{ \begin{matrix} y = 2\ \ \ \ \ \ \ \ \ \ \ \ \ \\ 4x - 14 = 2 \\ \end{matrix} \right.\ \]

\(\left\{ \begin{matrix} y = 2\ \ \ \ \ \\ 4x = 16 \\ \end{matrix} \right.\ \) \(\left\{ \begin{matrix} y = 2 \\ x = 4 \\ \end{matrix} \right.\ \)

\[Ответ:(4;2).\]

\[2)\ \left\{ \begin{matrix} 4y - x = 11\ \ \ \ \ \ \ \ \ \ \ \ \\ 5x - 2y = 17\ \ | \cdot 2 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 4y - x = 11\ \ \ \ \ \ \ \ \\ - 4y + 10x = 34 \\ \end{matrix} \right.\ \ \ +\]

\[\left\{ \begin{matrix} 9x = 45\ \ \ \ \ \ \ \\ 4y - x = 11 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 5\ \ \ \ \ \ \ \ \ \ \ \\ 4y - 5 = 11 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = 5\ \ \ \ \\ 4y = 16 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} x = 5 \\ y = 4 \\ \end{matrix} \right.\ \]

\[Ответ:(5;4).\]