Answer
Solution: $(2,5,\frac{1}{2})$
Work Step by Step
$x+y-4z = 5$ Equation $(1)$
$x-y+2z = -2$ Equation $(2)$
$3x+2y+4z = 18$ Equation $(3)$
Adding Equation $(1)$ and Equation $(2)$
$x+x+y-y-4z+2z = 5-2$
$2x-2z = 3$ Equation $(4)$
Multiplying Equation $(2)$ by $2$ and adding with Equation $(3)$
$2x +3x -2y +2y +4z + 4z = -4+18$
$5x +8z = 14$ Equation $(5)$
Multiplying Equation $(4)$ by $4$ and adding with Equation $(5)$
$8x+5x-8z+8z= 12+14$
$13x = 26$
$x = 2$
Substituting $x$ value in Equation $(4)$
$2(2) -2z = 3$
$4-2z = 3$
$-2z = 3-4$
$-2z = -1$
$z = \frac{-1}{-2}$
$z = \frac{1}{2}$
Substituting $x$ and $z$ values in Equation $(1)$
$x+y-4z = 5$
$2+y-4(\frac{1}{2}) = 5$
$2+y-2 = 5$
$y = 5$
Solution: $(2,5,\frac{1}{2})$