For what value of a, if any, will the following system of

For what value of a, if any, will the following system of equation in x, y and z have a solution?
2x + 3y = 4
x + y + z = 4
x + 2y – z = a

Augmented matrix is

R₁ → R₁ – 2R₂
R₃ → R₃ – R₂

R₁ → R₁ – R₃

will have solution if a = 0
as Rank of [A] = Rank of Augmented [A]