Chapter 9 - Section 9.1 - Solving Systems of Linear Equations in Three Variables and Problem Solving - Exercise Set - Page 637: 17

No solution

A: $x+2y-z=5$ B: $6x+y+z=7$ C: $2x+4y-2z=5$ $x+2y-z=2x+4y-2z$ $x+2y-z=2(x+2y-z)$ A+B $x+2y-z+6x+y+z=7+5$ $7x+3y=12$ 2B+C $2*(6x+y+z)+2x+4y-2z=7*2+5$ $12x+2y+2z+2x+4y-2z=14+5$ $14x+6y=19$ $7x+3y=12$ $14x+6y=19$ $2*(7x+3y)-(14x+6y)=2*12-19$ $14x+6y-14x-6y=24-19$ $0=5$ (false) Since we have a false statement, there is no solution to the system.