Question

$left { {log3x+log3y=3} atop {x-y+6=0}} right.$

Answer 1

$left { {{log_3xy=log_327} atop {x-y+6=0}} right. left { {{xy=27} atop {x=y-6}} right. \ \ (y-6)y=27 \ y^2-6y-27=0 \ D=36+108=144=12^2 \ y= frac{6pm12}{2} = left { {{y_1=-3} atop {y_2=9}} right. \ \ \ y_1=-3 \ -3x_1=27 => x_1=-9 \ x_1=-3-6=-9 \ \ y_2=9 \ 9x_2=27 => x_2=3 \ x_2=9-6=3$

Ответ: $left { {{x_1=-9} atop {y_1=-3}} right. left { {{x_2=3} atop {y_2=9}} right.$