Answer
$x=\frac{1}{3}$
$y=-\frac{1}{3}$
$z=\frac{2}{3}$
Work Step by Step
Express y from the first equation.
$y-z=-1 \rightarrow y=-1+z $
$6x+2y+z=2$
$-x-y-3z=-2$
Substitute $ y=-1+z$ into the second and the third equation.
$6x+2(-1+z)+z=2$
$-x-(-1+z)-3z=-2$
Simplify.
$6x+3z=4$
$-x-4z=-3$
Multiply the second equation by 6.
$-x-4z=-3 \rightarrow -6x-24z=-18$
Add the equations to eliminate x.
$-21z=-14$
$z=\frac{2}{3}$
Substitute for z and solve for y and x.
$y=-1+z \rightarrow y=-\frac{1}{3}$
$6x+3z=4 \rightarrow x=\frac{1}{3}$
