Final answer:
Newton's third law force pairs don't cancel each other out because they act on different systems. The system of interest in motion analysis determines which forces are considered, therefore, action-reaction forces don't cancel within a single system.
Step-by-step explanation:
Newton's third law of motion states that forces come in pairs of equal and opposite magnitude. However, these action-reaction force pairs do not cancel each other out when evaluating the motion of a system because they act on different systems. For instance, if a swimmer pushes against the wall of a pool, the push on the wall (the action) and the push back from the wall on the swimmer (the reaction) are equal and opposite. When we select the system of interest, such as the swimmer, only the forces acting on that system are considered in the motion analysis.
The key here is that the action-reaction forces are exerted on different objects, and that's why they don't cancel each other out for any single object's or system's motion. Therefore, if the swimmer is our system of interest, the force from the wall on the swimmer's feet moves the swimmer, while the force the swimmer exerts on the wall does not affect the swimmer's motion. This selection of the system of interest is crucial in analyzing problems using Newton's third law.