Answer
$(2, 1, 1)$
Work Step by Step
$4x+y-z=8$ Equation $(1)$
$x-y+2z=3$ Equation $(2)$
$3x-y+z=6$ Equation $(3)$
Equation $(1) +$Equation $(3)$
$(4x+y-z)+(3x-y+z)=(8+6)$
$7x=14$
$x=2$
Equation $(1) + $Equation $(2)$
$(4x+y-z)+(x-y+2z)=(8+3)$
$5x+z=11$ Equation $(4)$
Substitute $x=2$ into Equation $(4)$
$5(2)+z=11$
$10+z=11$
$z=1$
Substitute known values for $x$ and $z$ into Equation $(1)$ and solve for $y$.
$4(2)+y-1=8$
$7+y=8$
$y=1$
$(2, 1, 1)$ satisfies the given equations.
Solution is $(2, 1, 1)$
