Answer
$\{(1,3,-2)\}$
Work Step by Step
$\left\{\begin{array}{lllll}
x & +y & -z & =6 & \\
3x & -2y & +z & =-5 & /R_{2}=r_{2}+r_{1}\\
x & +3y & -2z & =14 & /R_{3}=r_{3}-2r_{1}
\end{array}\right.$
... Eliminate $z$ in eq. 2 and 3
$\left\{\begin{array}{lllll}
x & +y & -z & =6 & \\
4x & -y & & =1 & \\
-x & +y & & =2 & /R_{3}=r_{3}+r_{2}
\end{array}\right.$
... Eliminate y in equation 3
$\left\{\begin{array}{lllll}
x & +y & -z & =6 & (1)\\
4x & -y & & =1 & (2)\\
3x & & & =3 & (3)
\end{array}\right.$
$(3)\Rightarrow x=1$
$(2) \Rightarrow y=4x-1=4(1)-1=3$
$(1)\Rightarrow z=x+y-6=1+3-6=-2$
Solution set: $\{(1,3,-2)\}$
