Система уравнений {1/x-1/y=1/6 {x*y=6

$\left \{ {{ \frac{1}{x}- \frac{1}{y}= \frac{1}{6} } \atop {xy=6}} \right.$
ОДЗ: $x \neq 0,$ $y \neq 0$
$\left \{ {{ \frac{y-x}{xy}}= \frac{1}{6} } \atop {xy=6}} \right.$
$\left \{ {{{6(y-x)}{=xy}} } \atop {xy=6}} \right.$
$\left \{ {{{6(y-x)}{=6}} } \atop {xy=6}} \right.$
$\left \{ {y-x}{=1}} } \atop {xy=6}} \right.$
$\left \{ {y}{=1+x}} } \atop {x(1+x)=6}} \right.$
$\left \{ {y}{=1+x}} } \atop {x^2+x-6=0}} \right.$
$x^{2} +x-6=0$
$D=1^2-4*1*(-6)=25$
$x_1= \frac{-1+5}{2} =2,$ $y_1=2+1=3$
$x_2= \frac{-1-5}{2} =-3,$ $y_2=-3+1=-2$

Ответ: (2;3); (-3;-2)