Here are the championship scenarios...
Princeton beats or ties Penn: Nothing else matters, the Tigers would win the Ivy League title and earn the conference's outright berth.
Penn beats Princeton, Dartmouth ties or loses to Cornell: Penn and Princeton would tie for the title, both at 6-1-0, but the Quakers would earn the conference's NCAA Championship berth by virtue of winning the head-to-head meeting with the Tigers.
Penn beats Princeton, Dartmouth beats Cornell: The Big Green, Quakers and Tigers would be tri-champions, all of them at 6-1-0. (The teams would have gone 1-1-0 in head-to-head -- Princeton beat Dartmouth, Dartmouth beat Penn, Penn beat Princeton.) The conference's NCAA Championship berth would be decided by a random draw by the Ivy League's Executive Director, Robin Harris.