Question

Решите пж системы, сегодня нужно
1) lgx-lgy=2
x-10y=900
2) lgx-lgy=7
lgx+lgy=5

Answer 1

1) $left { {{lg(x/y)=2} atop {x-10y=900}} right.$
$left { {{x/y=100} atop {x-10y=900}} right.$
$left { {{x=100y} atop {x-10y=900}} right.$
100y-10y=900
90y=900
y=10
x=1000

2) $left { {{lg(x/y)=7} atop {lg(xy)=5}} right.$
$left { {{x/y=7} atop {xy=5}} right.$
$left { {{x=7y} atop {xy=5}} right.$
7y^2=5
y^2=5/7
y=+-sqrt{5/7}
y1=sqrt(5/7), x1=7sqrt(5/7)
y2=-sqrt(5/7), x2=-7sqrt(5/7)