ГДЗ по алгебре 7 класс Макарычев ФГОС Задание 1099

\[\boxed{\text{1099.}\text{\ }еуроки - ответы\ на\ пятёрку}\]

\[\textbf{а)}\ \left\{ \begin{matrix} x - 6y = 17 \\ 5x + 6y = 13 \\ \end{matrix} \right.\ ( + )\]

\[\left\{ \begin{matrix} 6x = 30 \rightarrow x = 5 \\ 5 - 6y = 17\ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[- 6y = 12\]

\[y = - 2\]

\[Ответ:(5;\ - 2).\]

\[\textbf{б)}\ \left\{ \begin{matrix} 4x - 7y = - 12 \\ - 4x + 3y = 12 \\ \end{matrix} \right.\ ( + )\]

\[\left\{ \begin{matrix} - 4y = 0 \rightarrow y = 0 \\ 4x - 7 \cdot 0 = - 12 \\ \end{matrix} \right.\ \]

\[4x = - 12\]

\[x = - 3\]

\[Ответ:( - 3;0).\]

\[\textbf{в)}\ \left\{ \begin{matrix} 3x + 2y = 5\ \ | \cdot ( - 1) \\ - 5x + 2y = 45\ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} - 3x - 2y = - 5 \\ - 5x + 2y = 45 \\ \end{matrix} \right.\ ( + )\]

\[\left\{ \begin{matrix} - 8x = 40 \rightarrow x = - 5 \\ - 5 \cdot ( - 5) + 2y = 45 \\ \end{matrix} \right.\ \]

\[2y = 45 - 25\]

\[2y = 20\ \]

\[\ y = 10\]

\[Ответ:( - 5;10).\]

\[\textbf{г)}\ \left\{ \begin{matrix} 9x - 4y = - 13\ \ \ | \cdot ( - 1) \\ 9x - 2y = - 20\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} - 9x + 4y = 13 \\ 9x - 2y = - 20 \\ \end{matrix} \right.\ \ \ \ ( + )\]

\[\left\{ \begin{matrix} 2y = - 7 \rightarrow y = - \frac{7}{2} = - 3,5 \\ 9x - 2 \cdot ( - 3,5) = - 20\ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[9x = - 27\]

\[x = - 3\]

\[Ответ:( - 3;\ - 3,5).\]