Answer
$(-\frac{1}{2},\frac{3}{4},1)$
Work Step by Step
Given Equations
$4y+2z=5$ Equation $(1)$
$2x+8y=5$ Equation $(2)$
$6x+4z=1$ Equation $(3)$
From Equation $(1)$
$4y+2z=5$
$4y=5-2z$
Substituting $4y=5-2z$ in Equation $(2)$
$2x+8y=5$
$2x+2(4y)=5$
$2x+2(5-2z)=5$
$2x+10-4z=5$
$2x-4z=5-10$
$2x-4z=-5$ Equation $(4)$
Adding Equation $(3)$ and Equation $(4)$
$6x+4z+2x-4z=1-5$
$8x=-4$
$x=-\frac{4}{8}$
$x=-\frac{1}{2}$
Substituting $x$ value in Equation $(2)$
$2x+8y=5$
$2(\frac{-1}{2})+8y=5$
$-1+8y=5$
$8y=6$
$y=\frac{6}{8}$
$y=\frac{3}{4}$
Substituting $x$ value in Equation $(3)$
$6x+4z=1$
$6(\frac{-1}{2})+4z=1$
$-3+4z=1$
$4z=4$
$z=1$
Solution: $(-\frac{1}{2},\frac{3}{4},1)$
