Answer
$[1/3, 0, -2]$
Work Step by Step
$3x-3y+z=-1$
$3x-y-z=3$
$-6x+4y+3z=-8$
$3x-3y+z=-1$
$3x-3y+z+(3x-y-z)=-1+3$
$3x-3y+z+3x-y-z=-2$
$6x-4y=2$
$-6x+4y+3z=-8$
$-6x+4y+3z+3*(3x-y-z)=-8+3*3$
$-6x+4y+3z+9x-3y-3z=-8+9$
$3x+y=1$
$6x-4y=2$
$6x-4y+4*(3x+y)=2+4*1$
$6x-4y+12x+4y=2+4$
$18x=6$
$18x/18 =6/18$
$x=1/3$
$6x-4y=2$
$6*1/3-4y=2$
$2-4y=2$
$2-4y+4y-2=2+4y-2$
$0=4y$
$0/4=4y/4$
$0=y$
$3x-y-z=3$
$3*1/3-0-z=3$
$1-0-z=3$
$1-z=3$
$1-z+z-3=3+z-3$
$-2=z$
