Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 939

\[1)\ \left\{ \begin{matrix} \frac{x - y}{5} - \frac{x + y}{2} = 10 \\ \frac{x}{5} + \frac{y}{2} = 10\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\frac{x}{5} + \frac{y}{2} = 10\]

\[\frac{y}{2} = 10 - \frac{x}{5}\]

\[y = 20 - 0,4x.\]

\[\frac{x - y}{5} - \frac{x + y}{2} = 10\]

\[\frac{x - (20 - 0,4x)}{5} - \frac{x + (20 - 0,4x)}{2} = 10\]

\[2(1,4x - 20) - 5(0,6x + 20) = 100\]

\[2,8x - 40 - 3x - 100 = 100\]

\[0,2x = - 240\]

\[x = - 1200;\]

\[y = 20 + 480 = 500.\]

\[Ответ:\ \ ( - 1200;\ 500).\]

\[2)\ \left\{ \begin{matrix} \frac{x + y}{2} + \frac{x - y}{3} = 6 \\ \frac{x + y}{4} - \frac{x - y}{3} = 0 \\ \end{matrix} \right.\ \]

\[\frac{x + y}{2} + \frac{x - y}{3} = 6\]

\[3(x + y) + 2(x - y) = 36\]

\[3x + 3y + 2x - 2y = 36\]

\[y = 36 - 5x.\]

\[\frac{x + y}{4} - \frac{x - y}{3} = 0\]

\[\frac{x + (36 - 5x)}{4} - \frac{x - (36 - 5x)}{3} = 0\]

\[3(36 - 4x) - 4(6x - 36) = 0\]

\[108 - 12x - 24x + 144 = 0\]

\[36x = 252\]

\[x = 7;\]

\[y = 36 - 35 = 1.\]

\[Ответ:\ \ (7;\ 1).\]