ГДЗ по алгебре 9 класс Макарычев ФГОС Задание 459

\(\boxed{\text{460.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\)

\[\left\{ \begin{matrix} 5x - y - 2 = 0\ \ \ \ \ \ \ \\ x^{2} - 2xy + y^{2} = 4 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} y = 5x - 2\ \ \\ (x - y)^{2} = 4 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} y = 5x - 2\ \ \ \ \ \ \ \ \ \ \ \ \\ (x - 5x + 2)^{2} = 4 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} y = 5x - 2\ \ \ \ \ \ \ \ \ \\ ( - 4x + 2)^{2} = 4 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} y = 5x - 2\ \ \ \ \ \\ (4x - 2)^{2} = 4 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} y = 5x - 2\ \ \ \ \\ (2x - 1)^{2} = 1 \\ \end{matrix} \right.\ \]

\[2x - 1 = 1\ \ \ \ \ \ \ \ \ 2x - 1 = - 1\]

\[2x = 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2x = 0\]

\[x = 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = 0\]

\[\Longrightarrow \left\{ \begin{matrix} x_{1} = 1 \\ y_{1} = 3 \\ \end{matrix} \right.\ \text{\ \ }или\ \ \ \left\{ \begin{matrix} x_{2} = 0\ \ \ \ \\ y_{2} = - 2. \\ \end{matrix} \right.\ \]

\[Ответ:(1;3);\ \ (0; - 2).\]