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МатематикаГДЗ по алгебре 7 класс Макарычев ФГОС Задание 1111
Задание 1111
\[\boxed{\text{1111.}\text{\ }еуроки - ответы\ на\ пятёрку}\]
\[\textbf{а)}\ \left\{ \begin{matrix} \frac{1}{3}x - \frac{1}{12}y = 4\ \ \ | \cdot 12 \\ 6x + 5y = 150\ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} 4x - y = 48\ \ | \cdot 5 \\ 6x + 5y = 150\ \ \ \ \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} 20x - 5y = 240 \\ 6x + 5y = 150\ \ \\ \end{matrix} \right.\ ( + )\]
\[\left\{ \begin{matrix} 26x = 390 \rightarrow x = 15 \\ y = 4x - 48\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} x = 15\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ y = 4 \cdot 15 - 48 \\ \end{matrix} \right.\ \]
\[y = 12\]
\[Ответ:(15;12).\]
\[\textbf{б)}\ \left\{ \begin{matrix} \frac{1}{3}v - \frac{1}{8}u = 3\ \ | \cdot 24 \\ 7u + 9v = - 2\ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} 8v - 3u = 72\ \ \ | \cdot 7 \\ 7u + 9v = - 2\ \ | \cdot 3 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} - 21u + 56v = 504 \\ 21u + 27v = - 6\ \ \ \ \\ \end{matrix} \right.\ ( + )\]
\[\left\{ \begin{matrix} 83v = 498 \rightarrow v = 6 \\ 3u = 8v - 72\ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[3u = 8 \cdot 6 - 72\]
\[u = \frac{48 - 72}{3} = - \frac{24}{3} = - 8\]
\[Ответ:(6;\ - 8).\]
\[\textbf{в)}\ \left\{ \begin{matrix} \frac{x}{4} + \frac{y}{6} = 1\ \ \ | \cdot 12 \\ 2x + 3y = - 12\ \ \ \ \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} 3x + 2y = 12\ \ \ | \cdot ( - 2) \\ 2x + 3y = - 12\ \ \ | \cdot (3) \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} - 6x - 4y = - 24 \\ 6x + 9y = - 36\ \ \ \\ \end{matrix} \right.\ ( + )\]
\[\left\{ \begin{matrix} 5y = - 60 \rightarrow y = - 12 \\ 2x = - 12 - 3y\ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[2x = - 12 - 3 \cdot ( - 12)\]
\[x = \frac{- 12 + 36}{2} = 12\]
\[Ответ:12;\ - 12).\]
\[\textbf{г)}\ \left\{ \begin{matrix} 4a - 5b - 10 = 0\ \ \ \ \\ \frac{a}{5} - \frac{b}{3} + \frac{1}{3} = 0\ \ | \cdot 15 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} 4a - 5b = 10\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 3a - 5b + 5 = 0\ \ | \cdot ( - 1) \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} 4a - 5b = 10 \\ - 3a + 5b = 5 \\ \end{matrix} \right.\ ( + )\]
\[\left\{ \begin{matrix} a = 15\ \ \ \ \ \ \ \ \ \ \ \\ 5b = 3a + 5 \\ \end{matrix} \right.\ \]
\[5b = 3 \cdot 15 + 5\]
\[b = \frac{50}{5} = 10\ \]
\[Ответ:(15;10).\]
