Question 1049713
If there was a solution, we could use the change of variables
{{{system(X=1/x,Y=1/y,Z=1/z)}}} <--->{{{system(x=1/X,y=1/Y,z=1/Z)}}} ,
solve the system of equations {{{system(4X+Y+2Z=4,2X+3Y-Z=1,X+Y+Z=4)}}} ,
finding non-zero values for {{{X}}} , {{{Y}}} , and {{{Z}}} ,
and change variables back to find {{{x}}} , {{{y}}} , and {{{z}}} .
Solving the system above we luckily find non-zero values for the variables, 
{{{system(X=-1,Y=2,Z=3)}}} , so {{{highlight(system(x=-1,y=1/2,z=1/3))}}} .