System of equations has has no solution if $q > 0$, then what is the value of $q$?

Question

System of equations :
Qx + y + z = Q-1 , x + Qy + z =Q-1 , x + y + Qz = Q-1

Has no solution if $Q>0$ , then what is the value of $Q$?

I want to solve this using matrices , so I used an augmented matrix for these matrices . I tried converting them into a reduced row echelon form matrix ,but even after a certain amount of operations I’m not able to fully arrive at a matrix where i can successfully apply the gauss Jordan elimination method

Answer 1

Using the Gauss algorithm we get $$x=\frac{Q-1}{Q+2}=y=z$$