Answer
$x=\frac{1}{4}$
$y=\frac{1}{2}$
$z=-\frac{1}{2}$
Work Step by Step
Express y from the first equation.
$2y+4z=-1 \rightarrow y=-\frac{1}{2}-2z$
$-2x+y+2z=-1$
$4x-2y=0$
Substitute $ y=-\frac{1}{2}-2z$ into the second and the third equation.
$-2x+(-\frac{1}{2}-2z)+2z=-1$
$4x-2(-\frac{1}{2}-2z)=0$
Simplify.
$-2x=-\frac{1}{2}$
$4x+1+4z=0$
From $-2x=-\frac{1}{2}$ we can express $ x=\frac{1}{4}$
Substitute $ x=\frac{1}{4}$ into $4x+1+4z=0$ to get the value of z.
$4(\frac{1}{4})+1+4z=0 \rightarrow z=-\frac{1}{2}$
Substitute $z=-\frac{1}{2}$ into $y=-\frac{1}{2}-2z$ to get the value of y.
$y=-\frac{1}{2}-2(-\frac{1}{2}) \rightarrow y=\frac{1}{2}$
