Answer
$(2,1,1)$
Work Step by Step
$2x-2y+4z = 6$ Equation $(1)$
$-4x-y+z = -8$ Equation $(2)$
$3x-y+z=6$ Equation $(3)$
Subtracting Equation $(3)$ from Equation $(2)$
$(-4x-y+z)-(3x-y+z) = -8 -6 $
$-4x-y+z-3x+y-z = -14$
$-7x = -14$
$x= 2$
Multiply Equation $(2)$ by $-2$ and add with Equation $(1)$
$-2(-4x-y+z) + 2x-2y+4z = -2(-8)+6$
$8x+2y-2z+2x-2y+4z = 16+6$
$10x+2z = 22$ Equation $(4)$
Substitute $x$ value in Equation $(4)$
$10x+2z = 22$
$10(2)+2z = 22$
$20+2z = 22$
$2z = 22-20$
$2z = 2$
$z= 1$
Substitute $x$ and $z$ values in Equation $(3)$
$3x-y+z=6$
$3(2)-y+(1)=6$
$6-y+1=6$
$7-y=6$
$7-6=y$
$y=1$
Solution: $(2,1,1)$
