Chapter 9 - Section 9.1 - Solving Systems of Linear Equations in Three Variables and Problem Solving - Exercise Set - Page 637: 18

No solution

A: $4x-y+3z=10$ B: $x+y-z=5$ C: $8x-2y+6z=10$ A+3B $4x-y+3z+3(x+y-z)=10+3*5$ $4x-y+3z+3x+3y-3z=10+15$ $7x+2y=25$ C+6B $8x-2y+6z+6(x+y-z)=10+6*5$ $8x-2y+6z+6x+6y-6z=10+30$ $14x+4y=40$ $7x+2y=25$ $14x+4y=40$ $-2*(7x+2y)+14x+4y=-2*25+40$ $-14x-4y+14x+4y=-50+40$ $0=-10$ (false) Since this statement is false, there is no solution to the system.