Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 33

\[\boxed{\mathbf{33}.}\]

\[1)\ \left\{ \begin{matrix} x - 3y = 5 - 0,2x - 20y\ \ \ \ \ \\ 0,5x - y - 2 = 2 - x - 20y \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 1,2x + + 17y = 5\ \ | \cdot ( - 5) \\ 1,5x + 19y = 4\ \ \ \ \ \ \ | \cdot 4\ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ }\]

\[\left\{ \begin{matrix} - 6x - 85y = - 25 \\ 6x + 76y = 16\ \ \ \ \ \ \ \\ \end{matrix} \right.\ ( + )\]

\[- 9y = - 9\]

\[y = 1.\]

\[1,5x + 19y = 4\]

\[1,5x = 4 - 19y\]

\[1,5x = 4 - 19 \cdot 1 = - 15\]

\[x = - 10.\]

\[Ответ:( - 10;1).\]

\[2)\ \left\{ \begin{matrix} 2x + 5 = 1 - x + 2y\ \ \ \ \\ 14x - 5 = 9x - 3y - 2 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 3x - 2y = - 4\ \ | \cdot 3 \\ 5x + 3y = 3\ \ \ \ \ | \cdot 2 \\ \end{matrix} \right.\ \text{\ \ \ \ }\]

\[\left\{ \begin{matrix} 9x - 6y = - 12 \\ 10x + 6y = 6\ \ \ \ \\ \end{matrix} \right.\ ( + )\]

\[19x = - 6\]

\[x = - \frac{6}{19}.\]

\[3x - 2y = - 4\]

\[2y = 3x + 4\]

\[2y = 3 \cdot \left( - \frac{6}{19} \right) + 4 =\]

\[= - \frac{18}{19} + 4 = 3\frac{1}{19}\]

\[2y = \frac{58}{19}\]

\[y = \frac{29}{19}.\]

\[Ответ:\left( - \frac{6}{19};\frac{29}{19} \right).\]

\[3)\ \left\{ \begin{matrix} 7x - 3y = - 2\ \ \ \ \ \ \ \ \\ - 8x + y = 12\ \ | \cdot 3 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[\left\{ \begin{matrix} 7x - 3y = - 2\ \ \ \ \ \\ - 24x + 3y = 36 \\ \end{matrix} \right.\ ( + )\]

\[- 17x = 34\]

\[x = - 2.\]

\[y = 12 + 8x\]

\[y = 12 + 8 \cdot ( - 2) = - 4.\]

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

\[Ответ:( - 2; - 4).\]

\[4)\ \left\{ \begin{matrix} \frac{1}{2}x + 3y = 1,5 \\ 0,5x - 2y = 4\ \\ \end{matrix} \right.\ ( - )\]

\[5y = - 2,5\]

\[y = - 0,5.\]

\[0,5x - 2y = 4\]

\[0,5x = 4 + 2y\]

\[0,5x = 4 + 2 \cdot ( - 0,5) = 3\]

\[x = 6.\]

\[Ответ:(6; - 0,5).\]

\[5)\ \left\{ \begin{matrix} 4x - 3y = - 3\ \ | \cdot ( - 2) \\ - 10x - 6y = 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ }\]

\[\ \left\{ \begin{matrix} - 8x + 6y = 6\ \ \\ - 10x - 6y = 3 \\ \end{matrix} \right.\ ( + )\]

\[- 18x = 9\]

\[x = - \frac{9}{18} = - \frac{1}{2}.\]

\[4x - 3y = - 3\]

\[3y = 4x + 3\]

\[3y = 4 \cdot \left( - \frac{1}{2} \right) + 3 = 1\]

\[y = \frac{1}{3}.\]

\[Ответ:\left( - 0,5;\frac{1}{3} \right).\]

\[6)\ \left\{ \begin{matrix} 10x + 3y = 0,1\ \ | \cdot 2 \\ 7x - 2y = 1,3\ \ \ \ \ | \cdot 3 \\ \end{matrix} \right.\ \text{\ \ \ \ }\]

\[\ \left\{ \begin{matrix} 20x + 6y = 0,2 \\ 21x - 6y = 3,9 \\ \end{matrix} \right.\ ( + )\]

\[41x = 4,1\]

\[x = 0,1.\]

\[10x + 3y = 0,1\]

\[3y = 0,1 - 10x\]

\[3y = 0,1 - 10 \cdot 0,1 = - 0,9\]

\[y = - 0,3.\]

\[Ответ:(0,1;\ - 0,3).\]