ГДЗ по алгебре 7 класс Макарычев ФГОС Задание 1189

\[\boxed{\text{1189.}\text{\ }еуроки - ответы\ на\ пятёрку}\]

\[\textbf{а)}\ \left\{ \begin{matrix} 5x - 4y = 1 \\ 3x + 1 = 13 \\ 7x - 5y = 1 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 3x = 12\ \ \ \ \ \ \ \ \ \\ 4y = 5x - 1 \\ 7x - 5y = 1 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[\ \left\{ \begin{matrix} x = 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 4y = 20 - 1 = 19 \\ 7x - 5y = 1\ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x = 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ y = \frac{19}{4}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ 5y = 7x - 1 \Longrightarrow \\ \end{matrix} \right.\ \]

\[5y = 28 - 1 = 27 \longrightarrow y =\]

\[= \frac{27}{5} \neq \frac{19}{4}:\]

\[значит,\ система\ не\ имеет\]

\[\ решений.\]

\[\textbf{б)}\ \left\{ \begin{matrix} 11x + 3y = 1\ \ \ \ \ \ \ \ \ \ \\ 2x + y = 3\ \ | \cdot ( - 3) \\ 5x + 2y = 4\ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} 11x + 3y = 1\ \ \ \\ - 6x - 3y = - 9 \\ 5x + 2y = 4\ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} 5x = - 8\ \ \ \ \ \ \\ y = 3 - 2x\ \\ 2y = 4 - 5x \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x = - \frac{8}{5}\text{\ \ \ \ \ \ \ \ \ } \\ y = 3 + \frac{2 \cdot 8}{5} \\ y = 2 + \frac{5}{2} \cdot \frac{8}{5} \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} x = - \frac{8}{5}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ y = 3 + 3,2 = 6,2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ y = 2 + \frac{8}{2} = 2 + 4 = 6 \neq 6,2 \\ \end{matrix} \right.\ \]

\[значит,\ система\ не\ имеет\]

\[\ решений.\]