Answer
$(0, 0.5, -4)$
Work Step by Step
$x+2y-z=5$ Equation $(1)$
$-3x-2y-3z=11$ Equation $(2)$
$4x+4y+5z=-18$ Equation $(3)$
Equation $(1)$ + Equation $(2)$
$(x+2y-z)+(-3x-2y-3z)=5+11$
$-2x-4z=16$ Equation $(4)$
$2\times$ Equation $(2)$ + Equation $(3)$
$2(-3x-2y-3z)+(4x+4y+5z)=2(11)+(-18)$
$(-6x-4y-6z)+(4x+4y+5z)=22-18$
$-2x-z=4$ Equation $(5)$
Equation $(4)$ $-$ Equation $(5)$
$(-2x-4z)-(-2x-z)=16-4$
$-3z=12$
$z=-4$
Substitute $z=-4$ into Equation $(5)$.
$-2x+4=4$
$-2x=0$
$x=0$
Substitute known values for $x$ and $z$ into Equation $(1)$.
$0+2y+4=5$
$2y=1$
$y=0.5$
$(0, 0.5, -4)$ satisfies the given equations.
Solution is $(0, 0.5, -4)$.