Question

решите систему управлений:​

Answer 1

решение способом замены

$\frac{6}{x + y} + \frac{5}{x - y} = 7 \\ \frac{3}{x + y} - \frac{2}{x - y} = - 1$

$\frac{1}{x + y} = t \\ \frac{1}{x - y} = k$

$6t + 5k = 7 \\ 3t - 2k = - 1$

$6t + 5k = 7 \\ - 6t + 4k = 2$

$9k = 9 \\ k = 1$

$\\ 3t - 2k = - 1 \\ 3t - 2 \times 1 = - 1 \\ 3t - 2 = - 1 \\ 3t = 1 \\ t = \frac{1}{3}$

$\frac{1}{x + y} = \frac{1}{3} \\ \frac{1}{x - y} = 1 \\ \\ x + y = 3 \\ x - y = 1 \\ \\ 2x = 4 \\ x = 2 \\ \\ 2 - y = 1 \\ - y = - 1 \\ y = 1$

Ответ: (х,у) = (2;1)