Question

Система уравнений

2log3 x-3 log3 y=-11
3log3 x+2log3 y=3

Answer 1

2log(3) x - 3 log(3) y = -11

3log(3) x + 2log(3) y = 3

ОДЗ x>0 y>0

умножаем первое на 2, второе на 3 и складываем

4log(3) x - 6 log(3) y = -22

9log(3) x + 6log(3) y = 9

4log(3) x - 6 log(3) y + 9log(3) x + 6log(3) y = -22 + 9

13log(3) x = -13

log(3) x = -1

x = 1/3

2*(-1) - 3log(3) y = -11

-3log(3) y = -9

log(3) y = 3

y = 27

Ответ {1/3, 27}