Chapter 9 - Section 9.1 - Solving Systems of Linear Equations in Three Variables and Problem Solving - Exercise Set - Page 637: 6

$(-3, -2, 5)$

A: $2x-3y+z=5$ B: $x+y+z=0$ C: $4x+2y+4z=4$ A+3B $2x-3y+z+3(x+y+z)=5+3*0$ $2x-3y+z+3x+3y+3z=5$ $5x+4z=5$ 2B-C $2*(x+y+z)-(4x+2y+4z)=2*0-4$ $2x+2y+2z-4x-2y-4z=-4$ $-2x-2z=-4$ $-2(x+z=2)$ $x+z=2$ $5x+4z=5$ $x+z=2$ $5x+4z-4(x+z)=5-4*2$ $5x+4z-4x-4z=5-8$ $x=-3$ $5x+4z=5$ $5*-3+4z=5$ $-15+4z=5$ $4z=20$ $4z/4=20/4$ $z=5$ $x+y+z=0$ $-3+y+5=0$ $y+2=0$ $y=-2$