Beis Shamai and Beis Hillel argue whether the Chagigah of the first day of Pesach must be brought from Chulin (Beis Shamai) or may even be brought from Ma'aser (Beis Hillel).

Question: Why are they discussing specifically the Chagigah of the first day of Pesach, if the same applies to the Chagigos of all festivals?

Answer: They mention the Chagigah of the Fifteenth of Nisan to teach that the Chagigah of that day is mid'Oraisa, to exclude the Chagigah of the Fourteenth of Nisan, which is only mid'Rabanan.

Question: Why does Beis Hillel say that the Chagigah of the first day of Pesach may be brought from Ma'aser -- it is an obligatory Korban, and all obligatory Korbanos must be brought from Chulin!?

Answer: Beis Hillel is referring to a case of "Tofel" -- adding Ma'aser to one's Chulin in order to have more meat (Beis Hillel permits "Tofel," while Beis Shamai maintains that the entire Korban must come from Chulin).

(Chizkiyah): One may combine an animal of Ma'aser with an animal of Chulin (to serve as the Korban Chagigah so that a large family has more meat to eat), but not money of Ma'aser with money of Chulin (to bring one large animal).

(R. Yochanan): One may combine money of Ma'aser with money of Chulin (to bring one large animal), but not an animal of Ma'aser with an animal of Chulin.

There are Beraisos which support both opinions.

"You shall rejoice in your festival" (Devarim 16:14) teaches that one fulfills the Mitzvah of Simchah with all types of Simchah-inducing meats.

This includes the meat of Korbanos Nedarim, Nedavos, and Ma'aser Behemah for a Yisrael.

For a Kohen, this also includes the meat of a Chatas, Asham, Bechor, and the Chazeh and Shok.

Question: Perhaps this also includes birds and flour offerings!?

Answer: The verse emphasizes, "You shall rejoice in your festival (b'Chagecha)," meaning that your Simchah shall come from whatever animal the Chagigah comes from, which excludes birds and flour.

(R. Ashi): The verse says, "You shall rejoice" -- the flesh of birds and flour do not bring a person to rejoice (while the meat of animals does).

Question: What does R. Ashi do with the phrase, "[You shall rejoice] in your festival?"

Answer: This teaches that during the festival, one may not marry, because the verse says that one must rejoice "in your festival" and not in your wife.

One who has many people to feed (in his family), but little property, should bring many Shelamim and few Olos.

One who has few people to feed, but lots of property, should bring many Olos and few Shelamim.

One who has few people to feed and little property, for such a person the minimum values of one Me'ah's worth (of Olos) and two Me'ah's worth (of Shelamim) apply.

One who has many people to feed and lots of property, for such a person the verse, "every man according to what he can give, according to the blessing that Hash-m gave you" (Devarim 16:17) applies.

Question: How can one who has many people to feed, but has little property, bring many Shelamim?

Answer: He is "Tofel" -- he combines Ma'aser with his Chulin to bring more animals.

(R. Chisda): He combines Ma'aser money with Chulin money to bring one big animal (like R. Yochanan on 8a).

(R. Sheshes): He may even combine Ma'aser animals with Chulin animals to bring many animals (a third opinion, not like Chizkiyah nor R. Yochanan on 8a).

(Reish Lakish): One who separated ten animals as his Korban Chagigah, and only had time to bring five on the first day of Yom Tov, may bring the remaining five on the second day.

(R. Yochanan): Since the day ended, he may no longer bring the remaining animals.

(R. Aba): Reish Lakish and R. Yochanan are not arguing.

Reish Lakish is referring to when the person specified that he separated all ten animals to be brought on the first day.

R. Yochanan is referring to when the person did not specify that the animals were all meant to be brought on the first day.

Furthermore, there was time left to bring them on the first day.

And he had family members to eat them as well.

The fact that he did not bring them shows that he intended all along to bring them on the second day (and thus there is a problem of Bal Tosif).