I Statement about torque in a system of particles

[SR_0301]

Hello guys, I’m studying Newton’s Mechanics at the first year of engineering, and I would like to ask one question about torque. In my book I found this statement ‘’ Given a system of particles, it’s always possible to determine a pair of forces which torque is indipedent from the pole chosen, and also a force which pass through the pole ( so its torque is 0 respect to that pole ). Unfortunately there aren't examples or a scratch of demonstration of the statement. I think I got the first part about the two forces, but I'm still a bit confused about the true utility. I know the fact that the torque of internal forces which are compatible with Newton third law is zero, and that's practically a consequence of this statement (because the torque is zero indipendently from the pole)

 

[Orodruin]

Two forces of equal magnitude that are opposite in direction and act along different lines are called a couple. Since they are equal in magnitude but opposite in direction they give a net force of zero, but a non-zero torque. This torque is independent from the reference point as, the torque is given by
$$
\vec \tau = \vec x_1 \times \vec F - \vec x_2 \times \vec F = (\vec x_1 - \vec x_2)\times \vec F
$$
and $\vec x_1 - \vec x_2$ is independent of the reference point.

You can summarize the forces acting on a system for any reference point by the total force, acting at that point, and a torque. If the total force is zero then the torque is independent of the reference point, if not it will change when you change reference. The total force is the same regardless of the reference point.