Решебник по алгебре 9 класс Макарычев Задание 1032

 

\[\boxed{\text{1032\ (1032).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ y = 2x - 11\ \ \ и\ \ \ y = - 5x + 3\]

\[2x - 11 = - 5x + 3\]

\[7x = 14\]

\[x = 2 \Longrightarrow \ \ y = 2 \cdot 2 - 11 = - 7.\]

\[Ответ:(2;\ - 7).\]

\[\textbf{б)}\ y = - 3x - 10\ \ \ и\ \ \]

\[y = x^{2} - 13x + 6\]

\[- 3x - 10 = x^{2} - 13x + 6\]

\[x^{2} - 10x + 16 = 0\]

\[D = 100 - 64 = 36,\]

\[x_{1} = \frac{10 + 6}{2} = 8,\ \ \]

\[x_{2} = \frac{10 - 6}{2} = 2.\]

\[1)\ x_{1} = 8 \Longrightarrow \ y_{1} = - 34.\]

\[2)\ x_{2} = 2 \Longrightarrow \ y_{2} = - 16.\]

\[Ответ:(8;\ - 34);\ \ (2;\ - 16).\]

\[\textbf{в)}\ y = - 3x^{2} + x - 3\ \ \ и\ \ \]

\[y = - x^{2} + x - 5\]

\[- 3x^{2} + x - 3 = - x^{2} + x - 5\]

\[- 2x^{2} + 2 = 0\]

\[x^{2} = 1\]

\[x = \pm 1.\]

\[1)\ x_{1} = 1 \Longrightarrow \ y_{1} = - 5.\]

\[2)\ x_{2} = - 1 \Longrightarrow \ y_{2} = - 7.\]

\[Ответ:(1;\ - 5);\ \ ( - 1;\ - 7).\]

\[\textbf{г)}\ y = 4x² + 3x + 6\ \ \ и\ \]

\[y = 3x² - 3x - 3\]

\[4x^{2} + 3x + 6 = 3x^{2} - 3x - 3\]

\[x^{2} + 6x + 9 = 0\]

\[D = 36 - 36 = 0\]

\[x = \frac{- 6 + 0}{2} = - 3 \Longrightarrow \ \ y = 33.\]

\[Ответ:( - 3;33).\]