Answer
$[12, 6, 4]$
Work Step by Step
$3/4*x-1/3*y+1/2*z=9$
$1/6*x+1/3*y-1/2*z=2$
$1/2*x-y+1/2*z=2$
$3/4*x-1/3*y+1/2*z=9$
$12*(3/4*x-1/3*y+1/2*z)=12*9$
$9x-4y+6z=108$
$1/6*x+1/3*y-1/2*z=2$
$6*(1/6*x+1/3*y-1/2*z)=6*2$
$x+2y-3z=12$
$1/2*x-y+1/2*z=2$
$2*(1/2*x-y+1/2*z)=2*2$
$x-2y+z=4$
$x+2y-3z=12$
$x+2y-3z-(x-2y+z)=12-4$
$x+2y-3z-x+2y-z=8$
$4y-4z=8$
$4y-4z+4z=8+4z$
$4y=8+4z$
$4y/4=(8+4z)/4$
$y=2+z$
$9x-4y+6z=108$
$9x-4y+6z-(9)(x-2y+z)=108-(9)(4)$
$9x-4y+6z-9x+18y-9z=108-36$
$14y-3z=72$
$14(2+z)-3z=72$
$28+14z-3z=72$
$28+11z=72$
$28+11z-28=72-28$
$11z=44$
$11z/11 =44/11$
$z=4$
$y=2+z$
$y=2+4$
$y=6$
$x-2y+z=4$
$x-2*6+4=4$
$x-12+4=4$
$x-12+4-4=4-4$
$x-12=0$
$x-12+12=0+12$
$x=12$
