Answer
Inconsistent.
Work Step by Step
Express x from the first equation.
$x-2y-3z=5 \rightarrow x=2y+3z+5$
$2x+y-z=5$
$4x-3y-7z=5$
Substitute $ x=2y+3z+5$ into the second and the third equation.
$2(2y+3z+5)+y-z=5$
$4(2y+3z+5)-3y-7z=5$
Simplify.
$5y+5z=-5$
$5y+5z=-15$
Multiply the first equation by -1.
$5y+5z=-5 \rightarrow -5y-5z=5$
Add these equations:
$-5y-5z=5$
$5y+5z=-15$
$0=-10$
After addition of the equations we got that $0=-10$ which is false. No values of x, y and z satisfy this equation and therefore the system is inconsistent.