ГДЗ по алгебре 7 класс Макарычев ФГОС Задание 1184

\[\boxed{\text{1184.}\text{\ }еуроки - ответы\ на\ пятёрку}\]

\[\textbf{а)}\ \left\{ \begin{matrix} 25x - 18y = 75\ \ \ \ \ \ \ \ \ \\ 5x - 4y = 5\ \ | \cdot ( - 5) \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 25x - 18y = 75\ \ \ \ \ \\ - 25x + 20y = - 25 \\ \end{matrix} \right.\ ( + )\]

\[\left\{ \begin{matrix} 2y = 50 \rightarrow y = 25\ \ \ \ \ \ \ \ \ \ \\ 5x = 5 + 4y = 5 + 4 \cdot 25 \\ \end{matrix} \right.\ \]

\[5x = 105\]

\[x = 21\]

\[Ответ:(21;25).\]

\[\textbf{б)}\ \left\{ \begin{matrix} 35x = 3y + 5\ \ \ \ \ \ \ \ \ | \cdot 4 \\ 49x = 4y + 9\ \ | \cdot ( - 3) \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 140x = 12y + 20\ \ \ \ \ \ \ \\ - 147x = - 12y - 27 \\ \end{matrix} \right.\ ( + )\]

\[\left\{ \begin{matrix} - 7x = - 7 \rightarrow x = 1 \\ 4y = 49x - 9\ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[4y = 49 - 9 = 40\]

\[y = 10\]

\[Ответ:(1;10).\]

\[\textbf{в)}\ \left\{ \begin{matrix} 8y - 5z = 23\ \ | \cdot ( - 2) \\ 3y - 2z = 6\ \ \ \ \ \ \ \ \ \ | \cdot 5 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} - 16y + 10z = - 46 \\ 15y - 10z = 30\ \ \ \ \ \ \\ \end{matrix} \right.\ ( + )\]

\[\left\{ \begin{matrix} - y = - 16 \rightarrow y = 16 \\ 2z = 3y - 6\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[2z = 3 \cdot 16 - 6\]

\[z = \frac{42}{2} = 21\ \]

\[Ответ:(16;21).\]

\[\textbf{г)}\ \left\{ \begin{matrix} 13x - 15y = - 48 \\ 2x + y = 29\ \ | \cdot 5\ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 13x - 15y = - 48 \\ 30x + 15y = 435 \\ \end{matrix} \right.\ ( + )\]

\[\left\{ \begin{matrix} 43x = 387 \rightarrow x = 9 \\ y = 29 - 2x\ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[y = 29 - 18 = 11\]

\[Ответ:(9;11).\]

\[\textbf{д)}\ \left\{ \begin{matrix} 7x + 4y = 74\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 3x + 2y = 32\ \ | \cdot ( - 2) \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 7x + 4y = 74\ \ \ \ \ \ \ \\ - 6x - 4y = - 64 \\ \end{matrix} \right.\ ( + )\]

\[\left\{ \begin{matrix} x = 10\ \ \ \ \ \ \ \ \ \ \ \ \\ 2y = 32 - 3x \\ \end{matrix} \right.\ \]

\[2y = 32 - 30 = 2\]

\[y = 1\]

\[Ответ:(10;1).\]

\[\textbf{е)}\ \left\{ \begin{matrix} 11u + 15v = 1,9\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ - 3u + 5v = 1,3\ \ | \cdot ( - 3) \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 11u + 15v = 1,9 \\ 9u - 15v = - 3,9 \\ \end{matrix} \right.\ ( + )\]

\[\left\{ \begin{matrix} 20u = - 2 \rightarrow u = - 0,1 \\ 5v = 1,3 + 3u\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[5v = 1,3 - 0,3 = 1\]

\[v = \frac{1}{5} = 0,2\]

\[Ответ:( - 0,1;0,2).\]