If a system is subjected to a zero resultant external force, its...

According to Newton's second law for a system of particles, the net external force is related to the acceleration of the centre of mass by the equation $\vec{F}_{ext} = M \vec{a}_{cm}$.

Given that the resultant external force is zero ($\vec{F}_{ext} = 0$), we get $\vec{a}_{cm} = 0$. Therefore, the centre of mass must not accelerate.

Since the acceleration is zero, the velocity of the centre of mass $\vec{v}_{cm}$ remains constant. This constant velocity can be either zero or non-zero. If the initial velocity is non-zero, the centre of mass will continue to move with that constant velocity. Thus, the centre of mass may move.