Answer
$\displaystyle \{(-3,\frac{1}{2},1)\}$
Work Step by Step
$\left\{\begin{array}{lllll}
x & +2y & -z & =-3 & \\
2x & -4y & +z & =-7 & /R_{2}=r_{2}-2r_{1}\\
-2x & +2y & -3z & =4 & /R_{3}=r_{3}+2r_{1}
\end{array}\right.$
... Eliminate $x$ in eq. 2 and 3
$\left\{\begin{array}{lllll}
x & +2y & -z & =-3 & \\
& -8y & +3z & =-1 & \\
& +6y & -5z & =-2 & /R_{3}=4r_{3}+3r_{2}
\end{array}\right.$
... Eliminate y in equation 3
$\left\{\begin{array}{lllll}
x & +2y & -z & =-3 & \\
& -8y & +3z & =-1 & \\
& & -11z & =-11 &
\end{array}\right.$
$(3)\Rightarrow z=1$
$(2) \displaystyle \Rightarrow-8y=-3z-1\Rightarrow-8y=-4\Rightarrow y=\frac{1}{2}$
$(1)\Rightarrow x=-2y+z-3=-1+1-3=-3$
Solution set: $\displaystyle \{(-3,\frac{1}{2},1)\}$
