Chapter 9 - Section 9.1 - Solving Systems of Linear Equations in Three Variables and Problem Solving - Exercise Set - Page 641: 55

$(1, -1, 2, 3)$

$x+y+z+w=5$ $2x+y+z+w=6$ $x+y+z=2$ $x+y=0$ $x+y+z-(x+y)=2-0$ $x+y+z-x-y=2$ $z=2$ $2x+y+z+w-(x+y+z+w)=6-5$ $2x+y+z+w-x-y-z-w=1$ $x=1$ $x+y=0$ $1+y=0$ $y=-1$ $x+y+z+w=5$ $1+(-1)+2+w=5$ $1-1+2+w=5$ $2+w=5$ $w=3$