Two systems which exert opposite influence on the same set of organs are
Sympathetic and parasympathetic systems
Two systems which exert opposite influence on the same set of organs are the sympathetic nervous system and the parasympathetic nervous system. Both of these systems control involuntary activities which either prepare the body for a 'flight or fight' response or to relax the body after the danger is surpassed. For example, the sympathetic system increases contraction and rate of heartbeat (prepares us for fight or flight) while the parasympathetic system decreases the contraction and rate of heartbeat (relaxes the body).