Chapter 9 - Section 9.1 - Solving Systems of Linear Equations in Three Variables and Problem Solving - Exercise Set - Page 637: 5

$(-2, 3, -1)$

A: $2x+2y+z=1$ B: $-x+y+2z=3$ C: $x+2y+4z=0$ B+C $-x+y+2z+x+2y+4z=3+0$ $3y+6z=3$ $3(y+2z=1)$ $y+2z=1$ A+2B $2x+2y+z+2*(-x+y+2z)=1+2*3$ $2x+2y+z-2x+2y+4z=1+6$ $4y+5z=7$ $y+2z=1$ $4y+5z=7$ $4y+5z=7$ $-4(y+2z=1)$ $4y+5z-4y-8z=7-4$ $-3z=3$ $-3z/-3 = 3/-3$ $z=-1$ $y+2z=1$ $y+2*(-1)=1$ $y-2=1$ $y=3$ $2x+2y+z=1$ $2x+2*3-1=1$ $2x+6-1=1$ $2x+5=1$ $2x=-4$ $2x/2=-4/2$ $x=-2$