Question 259170
Use equation 1, 
{{{x+z=0}}}
{{{z=-x}}}
Substitute this value in eqs.2 and 3,
{{{x+y+2z=3}}}
{{{x+y-2x=3}}}
4.{{{-x+y=3}}}
.
.
.
{{{y+z=2}}}
{{{y-x=2}}}
5.{{{-x+y=2}}}
As you see eqs. 4 and 5 have the same left hand side and different right hand side. The system of equations is inconsistent. 
No solution.