How does Katniss solve the conflict in The Hunger Games?

Well, the problem is never really SOLVED until the last book, but in the end of The Hunger Games, she decides that they are not just one piece in the Capitol's games, so she and Peeta each take a Nightlock berry (the poisonous one used to kill Foxface) and eat it at the same time. They both live after being announced the winners, but the trouble only begins for Katniss...