Chapter 9 - Section 9.1 - Solving Systems of Linear Equations in Three Variables and Problem Solving - Exercise Set - Page 641: 52

$[1, 1, -7]$

$x+3y+z=-3$ $-x+y+2z=-14$ $3x+2y-z=12$ $x+3y+z=-3$ $-x+y+2z=-14$ $x+3y+z+(-x+y+2z)=-3+(-14)$ $x+3y+z-x+y+2z=-17$ $4y+3z=-17$ $-x+y+2z=-14$ $3x+2y-z=12$ $-x+y+2z=-14$ $3*(-x+y+2z=-14)$ $-3x+3y+6z=-42$ $-3x+3y+6z=-42$ $3x+2y-z=12$ $-3x+3y+6z+(3x+2y-z)=-42+12$ $-3x+3y+6z+3x+2y-z=-30$ $5y+5z=-30$ $(5y+5z)/5 =-30/5$ $y+z=-6$ $4y+3z=-17$ $y+z=-6$ $4y+3z=-17$ $y+3y+3z=-17$ $y+3(y+z)=-17$ $y+3(-6)=-17$ $y-18=-17$ $y-18+18=-17+18$ $y=1$ $y+z=-6$ $1+z=-6$ $1+z-1=-6-1$ $z=-7$ $x+3y+z=-3$ $x+3*1+(-7)=-3$ $x+3-7=-3$ $x-4=-3$ $x-4+4=-3+4$ $x=1$ $[1, 1, -7]$ $x/2 + y/3 + z/9$ $1/2 + 1/3 -7/9$ $1*9/2*9 + 1*6/3*6 - 7*2/9*2$ $9/18 + 6/18 - 14/18$ $15/18 - 14/18$ $1/18$