Answer
$x=1$
$ y=2$
$z=1$
Work Step by Step
Express x from the first equation.
$x+y+z=4 \rightarrow x=4-y-z$
$x+3y+3z=10$
$2x+y-z=3$
Substitute $ x=4-y-z$ into the second and the third equation.
$4-y-z+3y+3z=10$
$2(4-y-z)+y-z=3$
Simplify.
$2y+2z=6$
$-y-3z=-5$
Multiply the second equation by 2.
$-y-3z=-5 \rightarrow -2y-6z=-10$
Add the equations to eliminate y.
$-4z=-4$
$z=1$
Substitute for z and solve for x and y.
$-y-3z=-5 \rightarrow y=2$
$ x=4-y-z\rightarrow x=1$
