Chapter 9 - Section 9.1 - Solving Systems of Linear Equations in Three Variables and Problem Solving - Exercise Set - Page 641: 54

$(5, 1, -2, 1)$

$5x+4y=29$ $y+z-w=-2$ $5x+z=23$ $y-z+w=4$ $y+z-w+y-z+w=-2+4$ $2y=2$ $2y/2=2/2$ $y=1$ $5x+4y=29$ $5x+4*1=29$ $5x+4=29$ $5x=25$ $5x/5=25/5$ $x=5$ $5x+z=23$ $5*5+z=23$ $25+z=23$ $z=-2$ $y-z+w=4$ $1-(-2)+w=4$ $1+2+w=4$ $3+w=4$ $w=1$