ГДЗ по алгебре 9 класс Макарычев ФГОС Задание 384

\[\boxed{\text{385.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]

\[\textbf{а)}\ \left\{ \begin{matrix} x^{2} + y^{2} = 16 \\ x - y = 4\ \ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} x = y + 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ (y + 4)^{2} + y^{2} = 16 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} x = y + 4\ \ \ \ \ \\ y(y + 4) = 0 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} y_{1} = 0 \\ x_{1} = 4 \\ \end{matrix} \right.\ \text{\ \ }или\ \ \left\{ \begin{matrix} y_{2} = - 4 \\ x_{2} = 0\ \ \ . \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x^{2} + y^{2} = 16 \\ x - y = 4\ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x^{2} + y^{2} = 16 \\ y = x - 4\ \ \ \ \ \ \\ \end{matrix} \right.\ \]

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

\[\Longrightarrow \left\{ \begin{matrix} y = x^{2} + 1\ \ \ \ \ \ \ \ \ \\ 2x^{2} + x - 3 = 0 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} x_{1} = 1 \\ y_{1} = 2 \\ \end{matrix} \right.\ \text{\ \ \ }или\ \ \ \left\{ \begin{matrix} x_{2} = - 1,5 \\ y_{2} = 3,25. \\ \end{matrix} \right.\ \]

\[Ответ:а)\ (4;0);(0;\ - 4);\ \ \ \]

\[\textbf{б)}\ (1;2);\ \ ( - 1,5;3,25).\]