ГДЗ по алгебре 7 класс Макарычев ФГОС Задание 1101

\[\boxed{\text{1101.}\text{\ }еуроки - ответы\ на\ пятёрку}\]

\[\textbf{а)}\ \left\{ \begin{matrix} 12x - 7y = 2\ \ \ \ \ \ \ \ \ \ \ \ \\ 4x - 5y = 6\ \ | \cdot ( - 3) \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 12x - 7y = 2\ \ \ \ \ \ \ \ \ \ \ \ \\ - 12x + 15y = - 18 \\ \end{matrix} \right.\ ( + )\]

\[\left\{ \begin{matrix} 8y = - 16 \rightarrow y = - 2 \\ 12x - 7 \cdot ( - 2) = 2\ \ \ \\ \end{matrix} \right.\ \]

\[12x = 2 - 14\]

\[12x = - 12\]

\[x = - 1\]

\[Ответ:( - 1;\ - 2).\]

\[\textbf{б)}\ \left\{ \begin{matrix} 7u + 2v = 1\ \ | \cdot ( - 3) \\ 17u + 6v = - 9\ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} - 21u - 6v = - 3 \\ 17u + 6v = - 9\ \ \\ \end{matrix} \right.\ ( + )\]

\[\left\{ \begin{matrix} - 4u = - 12 \rightarrow u = 3 \\ 7 \cdot 3 + 2v = 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[2v = 1 - 21\]

\[2v = - 20\]

\[v = - 10\]

\[Ответ:(3;\ - 10).\]

\[\textbf{в)}\left\{ \begin{matrix} 6x = 25y + 1\ \ \ \ \ \ \ \ \ \ \ \ | \cdot 5 \\ 5x - 16y = - 4\ \ | \cdot ( - 6) \\ \end{matrix} \right.\ \ \]

\[\left\{ \begin{matrix} 30x - 125y = 5 \\ - 30x + 96y = 24 \\ \end{matrix} \right.\ ( + )\]

\[\left\{ \begin{matrix} - 29y = 29 \rightarrow y = - 1 \\ 6x = 25 \cdot ( - 1) + 1 \\ \end{matrix} \right.\ \]

\[6x = - 24\]

\[x = - 4\]

\[Ответ:( - 4;\ - 1).\]

\[\textbf{г)}\left\{ \begin{matrix} 4b + 7a = 90\ \ \ | \cdot 3 \\ 5a - 6b = 20\ \ \ | \cdot 2 \\ \end{matrix} \right.\ \ \]

\[\left\{ \begin{matrix} 12b + 21a = 270 \\ - 12b + 10a = 40\ \\ \end{matrix} \right.\ ( + )\]

\[\left\{ \begin{matrix} 31a = 310 \rightarrow a = 10 \\ 4b + 7 \cdot 10 = 90\ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[4b = 20\]

\[b = 5\]

\[Ответ:(10;5).\]