Row Reduction & Rank · Hard problem

For which value of $k$ is the system $A\mathbf x = \mathbf b$ with $A = \begin{pmatrix}4 & -1\\4 & 3\\-2 & 1\end{pmatrix}$ and $\mathbf b = \begin{pmatrix}1\\13\\k\end{pmatrix}$ consistent?