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МатематикаГДЗ по алгебре 7 класс Макарычев ФГОС Задание 1085
Задание 1085
\[\boxed{\text{1085.}\text{\ }еуроки - ответы\ на\ пятёрку}\]
\[\textbf{а)}\ \left\{ \begin{matrix} y - 2x = 1 \\ 6x - y = 7 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} y = 1 + 2x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2) \\ 6x - (1 + 2x) = 7\ \ (1) \\ \end{matrix} \right.\ \]
\[(1)\ 6x - 1 - 2x = 7\]
\[4x = 8\]
\[x = 2\]
\[(2)\ y = 1 + 2 \cdot 2\]
\[y = 5\]
\[Ответ:(2;5).\]
\[\textbf{б)}\ \left\{ \begin{matrix} 7x - 3y = 13 \\ x - 2y = 5\ \ \ \ \ \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} x = 5 + 2y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2) \\ 7 \cdot (5 + 2y) - 3y = 13\ \ \ (1) \\ \end{matrix} \right.\ \]
\[(1)\ \ \ \ 35 + 14y - 3y = 13\]
\[11y = - 22\]
\[y = 2\]
\[(2)\ \ x = 5 + 2 \cdot ( - 2)\]
\[x = 1\]
\[Ответ:(1;\ - 2).\]
\[\textbf{в)}\ \left\{ \begin{matrix} x + y = 6\ \ \ \ \\ 3x - 5y = 2 \\ \end{matrix} \right.\ \text{\ \ \ }\]
\[\left\{ \begin{matrix} x = 6 - y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2) \\ 3 \cdot (6 - y) - 5y = 2\ \ \ \ \ \ \ (1) \\ \end{matrix} \right.\ \]
\[(1)\ \ \ 18 - 3y - 5y = 2\]
\[- 8y = - 16\]
\[y = 2\]
\[(2)\ \ \ \ x = 6 - 2\]
\[x = 4\]
\[Ответ:\ \ \ (4;2).\]
\[\textbf{г)}\ \left\{ \begin{matrix} 4x - y = 11\ \ \\ 6x - 2y = 13 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} y = 4x - 11\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2) \\ 6x - 2 \cdot (4x - 11) = 13\ \ \ \ (1) \\ \end{matrix} \right.\ \]
\[(1)\ 6x - 8x + 22 = 13\]
\[- 2x = - 9\]
\[x = 4,5\]
\[(2)\ \ \ y = 4 \cdot 4,5 - 11\]
\[y = 7\]
\[Ответ:(4,5;7).\]
\[\textbf{д)}\ \left\{ \begin{matrix} y - x = 20\ \ \ \ \ \ \ \ \ \\ 2x - 15y = - 1 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} y = 20 + x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2) \\ 2x - 15 \cdot (20 + x) = - 1\ \ \ \ (1) \\ \end{matrix} \right.\ \]
\[(1)2x - 300 - 15x = - 1\]
\[- 13x = 299\]
\[x = - 23\]
\[(2)\ \ \ y = 20 - 23\]
\[y = - 3\]
\[Ответ:( - 23;\ - 3).\]
\[\textbf{е)}\ \left\{ \begin{matrix} 25 - x = - 4y \\ 3x - 2y = 30 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} x = 25 + 4y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2) \\ 3 \cdot (25 + 4y) - 2y = 30\ \ \ \ (1) \\ \end{matrix} \right.\ \]
\[(1)\ \ \ \ \ 75 + 12y - 2y = 30\]
\[10y = - 45\]
\[y = - 4,5\]
\[(2)\ \ \ x = 25 + 4 \cdot ( - 4,5)\]
\[x = 7\]
\[Ответ:\ \ \ (7;\ - 4,5).\]
