X≠0, y≠0
x-y=6
x=6+y
(6+y)/y + y/(6+y) = 10/3
((6+y)²+y²) / y(6+y) = 10/3
3((6+y)²+y²) = 10y(6+y)
108+36y+6y² = 60y+10y²
4y²+24y-108=0
y²+6y-27=0
D=36-4*(-27)=36+108=144=12²
y1=(-6+12)/2=6/2=3
y2=(-6-12)/2=-18/2=-9
x1=6+3=9
x2=6+(-9)=6-9=-3
ответ: (9;3) (-3;-9)