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МатематикаРешебник по алгебре 7 класс Макарычев ФГОС Задание 1237
Задание 1237
\[\boxed{\text{1237.}\text{\ }еуроки - ответы\ на\ пятёрку}\]
\[\textbf{а)}\ \left\{ \begin{matrix} x - y = - 1 \\ y - z = - 1 \\ z + x = 8 \\ \end{matrix} + \right.\ \text{\ \ \ \ \ \ \ \ \ }\]
\[\ \left\{ \begin{matrix} 2x = 6 \\ x - y = - 1 \\ z + x = 8 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} x = 3\ \ \ \ \ \ \ \ \ \\ 3 - y = - 1 \\ z + 3 = 8\ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 3 \\ y = 4 \\ z = 5 \\ \end{matrix} \right.\ \]
\[Ответ:x = 3,\ y = 4,\ z = 5.\ \]
\[\textbf{б)}\ \left\{ \begin{matrix} x + y = - 3 \\ y + z = 6 \\ z + x = 1 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} y = - 3 - x \\ y = 6 - z \\ z = 1 - x \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]
\[\text{\ \ }\left\{ \begin{matrix} y = - 3 - x \\ - 3 - x = 6 - 1 + x \\ z = 1 - x \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} y = - 3 - x \\ - 2x = 5 + 3 \\ z = 1 - x \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\]
\[\text{\ \ \ \ }\left\{ \begin{matrix} y = - 3 - x \\ x = - 4\ \ \ \ \\ z = 1 + 4 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} y = - 3 + 4 \\ x = - 4\ \ \ \ \\ z = 5\ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} y = 1 \\ x = - 4 \\ z = 5\ \\ \end{matrix} \right.\ \]
\[Ответ:x = - 4,\ y = 1,\ z = 5.\ \]
\[\textbf{в)}\ \left\{ \begin{matrix} x - y + 2z = 1 \\ x - y - z = - 2 \\ 2x - y + z = - 1 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ }\]
\[\text{\ \ }\left\{ \begin{matrix} x - y = 1 - 2z \\ (x - y) - z = - 2 \\ 2x - y + z = - 1 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} x - y = 1 - 2z \\ 1 - 2z - z = - 2 \\ 2x - y + z = - 1 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} x - y = 1 - 2z \\ 1 - 3z = - 2\ \ \ \\ 2x - y + z = - 1 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\]
\[\ \left\{ \begin{matrix} x - y = 1 - 2z \\ 3z = 3\ \ \ \ \ \ \ \ \ \ \ \\ 2x - y + z = - 1 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} z = 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x - y = 1 - 2 \cdot 1 \\ 2x - y + 1 = - 1 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} z = 1 \\ x - y = - 1 \\ 2x - y = - 2 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ }\]
\[\text{\ \ }\left\{ \begin{matrix} z = 1 \\ y = x + 1 \\ 2x - x - 1 = - 2 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]
\[\text{\ \ }\left\{ \begin{matrix} z = 1 \\ x = - 1 \\ y = - 1 + 1 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} z = 1 \\ x = - 1 \\ y = 0 \\ \end{matrix} \right.\ \]
\[Ответ:x = - 1,\ y = 0,\ z = 1.\ \]
