Answer
$[1, 2, 3, 4]$
Work Step by Step
$2x-z=-1$
$y+z+w=9$
$y-2w=-6$
$x+y=3$
$2x-z=-1$
$2*(2x-z=-1)$
$4x-2z=-2$
$y+z+w=9$
$2*(y+z+w=9)$
$2y+2z+2w=18$
$4x-2z+(2y+2z+2w)+(y-2w)+(x+y)=-2+(18)+(-6)+(3)$
$4x-2z+2y+2z+2w+y-2w+x+y=-2+18-6+3$
$4x+x+2y+y+y-2z+2z+2w-2w=13$
$5x+4y=13$
$5x+4y=13$
$x+4x+4y=13$
$x+4(x+y)=13$
$x+4(3)=13$
$x+12=13$
$x+12-12=13-12$
$x=1$
$x+y=3$
$1+y=3$
$1+y-1=3-1$
$y=2$
$2x-z=-1$
$2*1-z=-1$
$2-z=-1$
$2-z+z+1=-1+z+1$
$3=z$
$y+z+w=9$
$2+3+w=9$
$5+w=9$
$5+w-5=9-5$
$w=4$
