Chapter 4 - Sections 4.1-4.3 - Integrated Review - Systems of Linear Equations - Page 234: 17

Solution set is empty set $\{\}$.

$2x+4y-6z = 3$ Equation $(1)$ $-x+y-z=6 $ Equation $(2)$ $x+2y-3z = 1$ Equation $(3)$ Multiply Equation $(3)$ by $-2$ $-2x-4y+6z = -2$ Equation $(4)$ Add Equation $(1)$ and Equation $(4)$ $2x-2x+4y-4y-6z+6z = 3-2$ $0= 1$ Since this statement is false, the system of equations is inconsistent and has no solution.