Answer
No Solution.
Work Step by Step
$x+2y-z=5$ Equation $(1)$
$6x+y+z=7$ Equation $(2)$
$2x+4y-2z=5$ Equation $(3)$
Add Equation $(1)$ and Equation $(2)$
$x+2y-z+6x+y+z=5+7$
$7x+3y=12$ Equation $(4)$
Multiply Equation $(2)$ by $2$ and add with Equation $(3)$
$2(6x+y+z)+2x+4y-2z=2(7)+5$
$12x+2y+2z+2x+4y-2z=14+5$
$14x+6y=19$ Equation $(5)$
Multiply Equation $(4)$ by $-2$ and add with Equation $(5)$
$-2(7x+3y)+14x+6y=-2(12)+19$
$-14x-6y+14x+6y=-24+19$
$0=-5$
Since this statement is not true, the equations are parallel and have no solution.
