Answer
$(\frac{1}{2},0,\frac{3}{4})$
Work Step by Step
$2x+4y=1$ Equation $(1)$
$4x-4z=-1$ Equation $(2)$
$y-4z=-3$ Equation $(3)$
Subtracting Equation $(3)$ from Equation $(2)$
$4x-(y)-4z-(-4z)=-1-(-3)$
$4x-y-4z+4z=-1+3$
$4x-y = 2 $ Equation $(4)$
Multiplying Equation $(4)$ by $4$ then add with Equation $(1)$
$4x(4)+2x-y(4)+4y = 2(4) + 1$
$16x+2x-4y+4y = 8 + 1$
$18x = 9$
$x = \frac{1}{2}$
Substituting $x$ value in Equation $(2)$
$4x-4z = -1$
$4(\frac{1}{2})-4z=-1$
$2-4z=-1$
$-4z=-1-2$
$-4z=-3$
$z = \frac{3}{4}$
Substituting $z$ value in Equation $(3)$
$y-4z=-3$
$y-4(\frac{3}{4})=-3$
$y-3=-3$
$y=-3+3$
$y=0$
Solution: $(\frac{1}{2},0,\frac{3}{4})$
