Complex sentence: There was no football team, and Wilson's basketball and baseball teams would play an exhibition schedule the first year, and then began their official Interhigh Series competition in the 1936 --' 37 school year.
Split into simpler sentences: There was no football team, and Wilson's basketball and baseball teams played an exhibition-only schedule the first year. The basketball and baseball teams began their official Inter-High Series competition in the 1936 --' 37 school year.