Answer
$\{(-3,0.5,1)\}$
Work Step by Step
We are given the system of equations:
$\begin{cases}
x+2y-z=-3\\
2x-4y+z=-7\\
-2x+2y-3z=4
\end{cases}$
Use the elimination method. Add the second equation to the first equation; then multiply the second equation by 3 and add it to the third, to eliminate $z$:
$\begin{cases}
x+2y-z+2x-4y+z=-3-7\\
-2x+2y-3z+3(2x-4y+z)=4+3(-7)
\end{cases}$
$\begin{cases}
3x-2y=-10\\
4x-10y=-17
\end{cases}$
Multiply the first equation by -5 and add it to the second to eliminate $y$ and determine $x$:
$-5(3x-2y)+4x-10y=-5(-10)-17$
$-15x+10y+4x-10y=33$
$-11x=33$
$x=-3$
Determine $y$:
$3x-2y=-10$
$3(-3)-2y=-10$
$2y=-9+10$
$y=0.5$
Determine $z$:
$x+2y-z=-3$
$-3+2(0.5)-z=-3$
$-3+1-z=-3$
$-2-z=-3$
$z=1$
The solution set of the system is:
$\{(-3,0.5,1)\}$
