Chapter 9 - Section 9.1 - Solving Systems of Linear Equations in Three Variables and Problem Solving - Exercise Set - Page 638: 28

$[-6, 12, -4]$

$1/3*x-1/4*y+z=-9$ $1/2*x-1/3*y-1/4*z=-6$ $x-1/2*y-z=-8$ $1/3*x-1/4*y+z=-9$ $12*(1/3*x-1/4*y+z)=-9*12$ $4x-3y+12z=-108$ $1/2*x-1/3*y-1/4*z=-6$ $12*(1/2*x-1/3*y-1/4*z)=-6*12$ $6x-4y-3z=-72$ $x-1/2*y-z=-8$ $2*(x-1/2*y-z)=-8*2$ $2x-y-2z=-16$ $4x-3y+12z=-108$ $6x-4y-3z=-72$ $2x-y-2z=-16$ $4x-3y+12z=-108$ $4x-3y+12z+(-2)(2x-y-2z)=-108+(-2)(-16)$ $4x-3y+12z-4x+2y+4z=-108+32$ $-y+16z=-76$ $6x-4y-3z=-72$ $6x-4y-3z+(-3)(2x-y-2z)=-72+(-3)(-16)$ $6x-4y-3z-6x+3y+6z=-72+48$ $-y+3z=-24$ $-y+16z-(-y+3z)=-76-(-24)$ $-y+16z+y-3z=-52$ $13z=-52$ $13z/13=-52/13$ $z=-4$ $-y+3z=-24$ $-y+3(-4)=-24$ $-y-12=-24$ $-y-12+y+24=-24+y+24$ $12=y$ $2x-y-2z=-16$ $2x-(12)-2(-4)=-16$ $2x-12+8=-16$ $2x-4=-16$ $2x-4+4=-16+4$ $2x=-12$ $2x/2=-12/2$ $x=-6$