I got these equations after Gauss-Jordan elimination from a linear equation system..Now is it consistent or non-consistent?

Question

x= 0

y-2z = 0

w= 1

Answer 1

consistent if plugging in to first equation

results in 0=0 (or k=k)

but if you started with four variables

it would be a more complete answer

if y or z was found to be a value (even zero)

as it is, y and z are only constrained to y=2z