Answer
the linear system is Inconsistent.
Work Step by Step
$\begin{cases}
x-2y-3z=5\\
2x+y-z=5\\
4x-3y-7z=5
\end{cases}$
Multiplying Equation 2 by -2 and adding it to Equation 3, results in new Equation 3.
$\begin{cases}
-4x-2y+2z=-10\\
4x-3y-7z=5\\
-- -- -- --\\
-5y-5z=-5
\end{cases}$
Multiplying Equation 1 by -2 and adding it to Equation 2, results in new Equation 2.
$\begin{cases}
-2x+4y+6z=-10\\
2x+y-z=5\\
-- -- --\\
5y+5z=-5
\end{cases}$
Adding new Equation 2 and new Equation 3.
$\begin{cases}
5y+5z=-5\\
-5y-5z=-5\\
-- -- --\\
0=-10
\end{cases}$
Therefore, the linear system is Inconsistent.