Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 902

\[1)\ 3y - x < 5;\text{\ \ \ }\]

\[x + y > 26;\text{\ \ \ }\]

\[3x - 2y < 46;\]

\[1)\ \left\{ \begin{matrix} 3y - x < 5\ \ \ \ \ | \bullet 3 \\ 3x - 2y < 46\ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 9y - 3x < 15 \\ 3x - 2y < 46 \\ \end{matrix}\ ( + ) \right.\ \]

\[7y < 61\]

\[y < 8\frac{5}{7}.\]

\[2)\ \left\{ \begin{matrix} x + y > 26\ \ \ \ \ | \bullet 3\ \ \ \ \ \ \ \ \ \ \ \ \\ 3x - 2y < 46\ \ \ \ \ | \bullet ( - 1) \\ \end{matrix} \right.\ \text{\ \ \ }\]

\[\left\{ \begin{matrix} 3x + 3y > 78\ \ \ \ \ \ \\ - 3x + 2y > - 46 \\ \end{matrix}\ ( + ) \right.\ \]

\[5y > 32\]

\[y > 6\frac{2}{5}.\]

\[y = 7:\]

\[21 - x < 5\]

\[x > 16.\ \]

\[x + 7 > 26\]

\[x > 19.\]

\[3x - 14 < 46\]

\[3x < 60\]

\[\text{\ x} < 20.\]

\[y = 8:\]

\[24 - x < 5\]

\[x > 19.\text{\ \ \ }\]

\[x + 8 > 26\]

\[x > 18.\]

\[3x - 16 < 46\]

\[3x < 62\ \]

\[x < 20\frac{2}{3}.\]

\[Ответ:\ \ x = 20;\ y = 8.\]

\[2)\ 3y - 5x > 16;\]

\[3y - x < 44;\]

\[3x - y > 1;\]

\[1)\ \left\{ \begin{matrix} 3y - 5x > 16\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 3y - x < 44\ \ \ \ \ | \bullet ( - 1) \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 3y - 5x > 16\ \ \ \ \\ - 3y + x > - 44 \\ \end{matrix}\ ( + ) \right.\ \]

\[- 4x > - 28\]

\[x < 7.\]

\[2)\ \left\{ \begin{matrix} 3x - y > 1\ \ \ \ \ | \bullet 3 \\ 3y - 5x > 16\ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ }\]

\[\left\{ \begin{matrix} 9x - 3y > 3\ \ \\ 3y - 5x > 16 \\ \end{matrix}\ ( + ) \right.\ \]

\[4x > 19\]

\[x > 4,75.\]

\[x = 5:\]

\[3y - 25 > 16\]

\[3y > 41\]

\[y > 13\frac{2}{3}.\]

\[3y - 5 < 44\]

\[3y < 49\]

\[y < 16\frac{1}{3}.\]

\[15 - y > 1\]

\[y < 14.\]

\[x = 6:\]

\[3y - 30 > 16\]

\[3y > 46\]

\[y > 15\frac{1}{3}.\]

\[3y - 6 < 44\]

\[3y < 50\]

\[y < 16\frac{2}{3}.\]

\[18 - y > 1\]

\[y < 17.\]

\[Ответ:\ \ x = 6;\ y = 16.\]