Answer
$(-4, 2, -1)$
Work Step by Step
$3x-y+z=-15$
$x+2y-z=1$
$2x+3y-2z=0$
$3x-y+z=-15$
$x+2y-z=1$
$3x-y+z+x+2y-z=-15+1$
$4x+y=-14$
$3x-y+z=-15$
$2x+3y-2z=0$
$2*(3x-y+z)+2x+3y-2z=2*(-15)+0$
$6x-2y+2z+2x+3y-2z=-30$
$8x+y=-30$
$4x+y=-14$
$8x+y=-30$
$8x+y-(4x+y)=-30-(-14)$
$8x+y-4x-y=-30+14$
$4x=-16$
$4x/4=-16/4$
$x=-4$
$4x+y=-14$
$4*-4+y=-14$
$-16+y=-14$
$-16+y+16=-14+16$
$y=2$
$3x-y+z=-15$
$3*-4-2+z=-15$
$-12-2+z=-15$
$-14+z=-15$
$-14+z+14=-15+14$
$z=-1$