Answer
$x=1$
$y=-3$
$z=2$
Work Step by Step
Express y from the third equation.
$x+y+z=0$
$-x+2y+5z=3$
$3x-y=6 \rightarrow y=3x-6$
Substitute $ y=3x-6$ into the first and the second equation.
$x+3x-6+z=0$
$-x+2(3x-6)+5z=3$
Simplify.
$4x+z=6$
$5x+5z=15$
Multiply the first equation by -5.
$4x+z=6 \rightarrow -20x-5z=-30$
Add the equations to eliminate z.
$-15x=-15$
$x=1$
Substitute for x and solve for y and z.
$ 9x+z=6\rightarrow z=2$
$ y=3x-6\rightarrow y=-3$
