Answer
$x=5$
$y=0$
$z=1$
Work Step by Step
Express x from the first equation.
$x-4z=1 \rightarrow x=1+4z $
$2x-y-6z=4$
$2x+3y-2z=8$
Substitute $ x=1+4z$ into the second and the third equation.
$2(1+4z)-y-6z=4$
$2(1+4z)+3y-2z=8$
Simplify.
$-y+2z=2$
$3y+6z=6$
Multiply the first equation by 3.
$-y+2z=2 \rightarrow -3y+6z=6$
Add the equations to eliminate y.
$12z=12$
$z=1$
Substitute for z and solve for x and y.
$x=1+4z \rightarrow x=5$
$-y+2z=2 \rightarrow y=0$
