Answer
$x=5$, $y=3$ and $z=-1$
Work Step by Step
For the first two equations:
$2x-3y+z=0$
$2x+y+z=12$
Multiply the first equation by $-1$
$-2x+3y-z=0$
$2x+y+z=12$
Add the first equation to the second equation:
$4y=12$
$y=3$
Substitute $y=3$ in the third equation:
$3-z=4$
$z=-1$
Substitute the value of $y$ and $z$ in the first equation to solve for $x$
$2x-3(3)+(-1)=0$
$2x-10=0$
$2x=10$
$x=5$
The results are: $x=5$, $y=3$ and $z=-1$