The augmented matrix is [A:b].

Given rank ([A:b])=4

Because the number of variables in the system is three so the rank of the coefficient matrix A is 3.

The condition for the system to be consistent(Have a solution) is that rank([A:b])=rank(A).

Here we see that rank([A:b]) is not equal to rank (A). So the given system is inconsistent i.e. no solution.