x + 2y + z = 0,-x + y + z = -4 , 2x + 3y + z = 1

x+2y+z=0
-x+y+z=-4 +
3y+2z=-4

2x+3y+z=1
2x+4y+2z=0 -
-y-z=1

3y+2z=-4 (1)
-y-z =0 (2)

3y+2z=-4
-2y-2z=0 +
y= -4

3y+2z=-4
3.-4+2z=-4
-12+2z=-4
2z=-4+12
2z=8
z=4
x+2y+z=0
x+2.-4+4=0
x+(-8)+4=0
x+(-4)=0
x=4