Answer
Inconsistent.
Work Step by Step
Express x from the second equation.
$-x+2y+5z=4$
$x-2z=0 \rightarrow x=2z$
$4x-2y-11z=2$
Substitute $ x=2z$ into the first and the third equation.
$-(2z)+2y+5z=4$
$4(2z)-2y-11z=2$
Simplify.
$2y+3z=4$
$-2y-3z=2$
Add the equations.
$0=6$
After simplification of the equations we got that $0=6$ which is false. No values of x, y and z satisfy this equation and therefore the system is inconsistent.