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МатематикаРешебник по алгебре 9 класс Мерзляк Задание 448
Задание 448
\[\boxed{\text{448\ (448).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[1)\ \left\{ \begin{matrix} 2x + y = 10\ \ | \cdot 2 \\ 4x - 7y = 2\ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} 4x + 2y = 20 \\ 4x - 7y = 2\ \ \\ \end{matrix} \right.\ \ \ \ \ -\]
\[\left\{ \begin{matrix} 9y = 18\ \ \ \ \ \ \ \ \\ 4x - 7y = 2 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\left\{ \begin{matrix} y = 2\ \ \ \ \ \ \ \ \ \ \ \ \ \\ 4x - 14 = 2 \\ \end{matrix} \right.\ \]
\(\left\{ \begin{matrix} y = 2\ \ \ \ \ \\ 4x = 16 \\ \end{matrix} \right.\ \) \(\left\{ \begin{matrix} y = 2 \\ x = 4 \\ \end{matrix} \right.\ \)
\[Ответ:(4;2).\]
\[2)\ \left\{ \begin{matrix} 4y - x = 11\ \ \ \ \ \ \ \ \ \ \ \ \\ 5x - 2y = 17\ \ | \cdot 2 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} 4y - x = 11\ \ \ \ \ \ \ \ \\ - 4y + 10x = 34 \\ \end{matrix} \right.\ \ \ +\]
\[\left\{ \begin{matrix} 9x = 45\ \ \ \ \ \ \ \\ 4y - x = 11 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 5\ \ \ \ \ \ \ \ \ \ \ \\ 4y - 5 = 11 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} x = 5\ \ \ \ \\ 4y = 16 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} x = 5 \\ y = 4 \\ \end{matrix} \right.\ \]
\[Ответ:(5;4).\]
\[3)\ \left\{ \begin{matrix} 2x - 9y = 11 \\ 7x + 9y = 25 \\ \end{matrix} \right.\ \ \ +\]
\[\left\{ \begin{matrix} 9x = 36\ \ \ \ \ \ \ \ \ \ \ \\ 2x - 9y = 11 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 4\ \ \ \ \ \ \ \ \ \ \ \ \\ 8 - 9y = 11 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]
\[\left\{ \begin{matrix} x = 4\ \ \ \ \ \\ - 9y = 3 \\ \end{matrix}\ \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} x = 4 \\ y = - \frac{1}{3} \\ \end{matrix} \right.\ \]
\[Ответ:\left( 4;\ - \frac{1}{3} \right).\]
\[4)\ \left\{ \begin{matrix} 3x - 2y = 1\ \ | \cdot 4 \\ 12x + 7y = - 26\ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\]
\[\ \left\{ \begin{matrix} 12x - 8y = 4\ \ \ \ \ \\ 12x + 7y = - 26 \\ \end{matrix} \right.\ \ \ \ -\]
\[\left\{ \begin{matrix} - 15y = 30\ \ \ \ \ \\ 12x - 8y = 4 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\left\{ \begin{matrix} y = - 2\ \ \ \ \ \ \ \ \ \ \\ 12x + 16 = 4 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]
\[\ \left\{ \begin{matrix} y = - 2\ \ \ \ \ \\ 12x = - 12 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\left\{ \begin{matrix} y = - 2 \\ x = - 1 \\ \end{matrix} \right.\ \]
\[Ответ:( - 1;\ - 2).\]
\[\boxed{\text{448.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[y = ax^{2} + bx + 7\ \ \]
\[x = - 2 \rightarrow \ \ y = 0;\ \]
\[x = 3 \rightarrow \ \ y = 0.\]
\[\left\{ \begin{matrix} 4a - 2b + 7 = 0\ \ | \cdot 3 \\ 9a + 3b + 7 = 0\ \ \ |\ \cdot 2 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} 12a - 6b + 21 = 0 \\ 18a + 6b + 14 = 0 \\ \end{matrix}\ \right.\ \ | +\]
\[30a + 35 = 0\]
\[a = - \frac{35}{30}\]
\[a = - \frac{7}{6}\]
\[- 4 \cdot \frac{7}{6} + b \cdot ( - 2) + 7 = 0\]
\[- \frac{14}{3} - 2b + 7 = 0\]
\[2b = \frac{21 - 14}{3}\]
\[2b = \frac{7}{3}\]
\[b = \frac{7}{6}\]
\[Ответ:\ a = - \frac{7}{6};\ \ b = \frac{7}{6}.\]
