x(x+y+z)=6 (1)
y(x+y+z)=12 (2)
z(x+y+z)=18 (3)
(1)/(2)
x/y=1/2
y=2x
(1)/(3)
x/z=1/3
z=3x
x(x+2x+3x)=6
6x^2=6
x=1 y=2 z=3
x=-1 y=-2 z=-3