ГДЗ по алгебре 9 класс Макарычев Задание 509

\[\boxed{\text{509\ (509).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ \left\{ \begin{matrix} x^{2} - 3xy + 14 = 0 \\ 3x^{2} + 2xy - 24 = 0 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} 2x^{2} - 6xy + 28 = 0 \\ 9x^{2} + 6xy - 72 = 0 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} 11x^{2} = 44\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x^{2} - 3xy + 14 = 0 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} x^{2} = 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x^{2} - 3xy + 14 = 0 \\ \end{matrix} \right.\ \Longrightarrow\]

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

\[\textbf{б)}\ \left\{ \begin{matrix} 2x^{2} - 6y = xy\ \ \ \ \ \ \\ 3x^{2} - 8y = 0,5xy \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} 6x^{2} - 18y = 3xy\ \ \ \ \\ - 6x^{2} + 16y = - xy \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} - 2y = 2xy\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 3x^{2} - 8y = x^{2} - 3y \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} 2y(x + 1) = 0 \\ 2x² = 5y\ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]

\[1)\left\{ \begin{matrix} y = 0 \\ x = 0 \\ \end{matrix} \right.\ ,\]

\[2)\ \left\{ \begin{matrix} x + 1 = 0 \\ y = \frac{2x^{2}}{5}\text{\ \ \ } \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = - 1\ \\ y = 0,4. \\ \end{matrix} \right.\ \]

\[Ответ:а)\ (2;3);( - 2;\ - 3);\ \ \]

\[\textbf{б)}\ (0;0);( - 1;0,4).\]