Chapter 9 - Section 9.1 - Solving Systems of Linear Equations in Three Variables and Problem Solving - Exercise Set - Page 637: 2

$(3, -3, 1)$

A: $x+y-z=-1$ B: $-4x-y+2z=-7$ C: $2x-2y-5z=7$ 2A-C $2*(x+y-z)-(2x-2y-5z)=2(-1)-7$ $2x+2y-2z-2x+2y+5z=-2-7$ $4y+3z=-9$ 4A+B $4*(x+y-z)+(-4x-y+2z)=4(-1)+(-7)$ $4x+4y-4z-4x-y+2z=-4-7$ $3y-2z=-11$ $3y-2z=-11$ $4y+3z=-9$ $3*(3y-2z)+2(4y+3z)=3*-11+2*(-9)$ $9y-6z+8y+6z=-33-18$ $17y = -51$ $17y/17 = -51/17$ $y=-3$ $4y+3z=-9$ $4*(-3)+3z=-9$ $-12+3z=-9$ $3z=3$ $3z/3 = 3/3$ $z=1$ $x+y-z=-1$ $x+(-3)-1=-1$ $x-3-1=-1$ $x-4=-1$ $x=3$