Chapter 9 - Section 9.1 - Solving Systems of Linear Equations in Three Variables and Problem Solving - Exercise Set - Page 637: 16

$(1, 2, -2)$

A: $5x+y+3z=1$ B: $x-y+3z=-7$ C: $-x+y=1$ A-C $5x+y+3z-(x-y+3z)=1-(-7)$ $5x+y+3z-x+y-3z=8$ $4x+2y=8$ $-x+y=1$ $4x+2y=8$ $4x+2y+4(-x+y)=8+4*1$ $4x+2y-4x+4y=12$ $6y=12$ $6y/6=12/6$ $y=2$ $-x+y=1$ $-x+2=1$ $2=1+x$ $1=x$ $5x+y+3z=1$ $5*1+2+3z=1$ $5+2+3z=1$ $7+3z=1$ $3z=-6$ $3z/3=-6/3$ $z=-2$