(Mishnah): When is the Chagigah brought together with the Pesach on the 14th? When it occurs on a weekday, in Taharah and when the Pesach is too small for the members of the group.

When it occurs on a weekday, when the Pesach is large enough for the group and in Tum'ah, a Chagigah is not brought with the Pesach.

The Chagigah came from flock or cattle, from sheep and goats, from male or females; it may be eaten for two days and one night.

(Gemara - Beraisa): The Chagigah of the 14th could be brought from money of Maaser Sheni.

R' Yaakov bar Acha quoting Shmuel bar Abba: This shows that the Chagigah was optional. If it would be obligatory, it could not be brought from money of Maaser!

Beraisa: The Chagigah that accompanied the Pesach was eaten first in order that the Pesach be eaten when satiated.

Question: Why must it be eaten when satiated?

Answer (R' Yosi bei R' Bun quoting R' Yaakov bar Dasayei): To prevent a person from coming to break a bone of the Pesach.

Beraisa: The Chagigah that accompanied the Peasch was burned together with it.

Question: Surely their timeframes are different as the Chagigah is eaten for two days and the Pesach is only eaten until midnight?!

Answer: Since the Chagigah was eaten at the same table as the Pesach, the Chagiga would also need to be burned within the same timeframe (as it was impossible that some of the flesh of the Pesach did not stick to it).

In fact, any other foods that was served at the same table as the Pesach also needed to be burned within the same timeframe as the Pesach.

R' Yosa: This shows that one who ate cheese and wishes to eat meat must destroy any remnants even of the bread that he ate with the cheese.