Gemara

(Rav Yehudah): We bless Borei Peri ha'Etz on olive oil.

Suggestion: The case is, he ingests the oil with bread.

Rejection: If so, the bread is Ikar (primary) and the oil is Tefel (secondary);

(Mishnah): The general rule is, if one eats a Tefel food together with an Ikar food, he blesses only on the Ikar, and this exempts the Tefel.

Answer: The case is, he drinks the oil mixed in Anigron (water in which beets were cooked).

The case is, his throat hurts him (so his main intent is for the oil);

41a (Beraisa): If one wants to eat a radish and an olive, he blesses on the radish, and exempts the olive.

Answer: The case is, the radish is primary. (He eats the olive just to weaken the sharpness of the radish.)

Question (Seifa - R. Yehudah): He blesses on the olive, for it is one of the seven species.

Surely, R. Yehudah does not argue with the above Mishnah (that one blesses only on the Ikar)!

(Beraisa - R. Yehudah): If he eats the olive due to the radish, he blesses on the radish and exempts the olive.

Answer: The Beraisa is abbreviated. Really R. Yehudah and Chachamim argue about something else, i.e. two species that have the same Berachah;

i. Chachamim say that he blesses on whichever he wants [and exempts the other]. R. Yehudah says, he blesses on the olive, for it is one of the seven species.

Rishonim

Tosfos (41a DH Aval): When they have different Berachos, R. Yehudah agrees that one blesses on whichever he wants, i.e. the Chaviv.

Rashba (Berachos 39a DH Chazar): The Yerushalmi says that one blesses on leeks (and not on the meat), for everything is Tefel to the vegetables. If not for this, one would bless on what is Chaviv.

Agur (298, cited in Beis Yosef OC 212 DH Kasav): The Or Zaru'a says that the radish exempts the olive only when the radish is Ikar and Chaviv (he prefers it). If the radish is Ikar but not Chaviv, he blesses on the olive and afterwards on the radish. It is better to say more Berachos. We do not uproot (omit) Berachos in such a case.

Even ha'Ozer (cited in Sha'arei Teshuvah 212:1): The Gemara (Yoma 70a) forbids extra Berachos in cases such as Keri'as ha'Torah, where one Berachah can exempt both of them. Tosfos (Menachos 36a DH Sach) and the Poskim say so about Tefilin and Shechitah. However, here (if he blesses only on the Ikar) he does not make the proper Berachah on the Tefel. It is better that he make the proper Berachah that Chachamim enacted on the Tefel than to exempt it through the Ikar.

Poskim

Shulchan Aruch (OC 212:1): Even bread, if it is Tefel, he blesses on the fish and exempts the bread, since it is Tefel.

Rema: Some say that if the Tefel is Chaviv (he prefers it), he blesses on it, and afterwards he blesses on the Ikar.

Taz (3): This is from the Agur. Do not ask from Tosfos in Menachos (36a DH Sach), who says that if one talked in between putting on the Tefilin Shel Yad and the Shel Rosh, he caused himself to bless an unnecessary Berachah, for one Berachah could have exempted both. There, he need not talk in between. He caused an unnecessary Berachah. It seems that 'we do not uproot Berachos in such a case' answers why this is different than equal Berachos. There, we say that he blesses on one and exempts the other (211:1). Here, one could exempt both through one Berachah. He teaches that in such a case, when there are different Berachos (Borei Peri ha'Etz and Borei Peri ha'Adamah), and each has an attribute over the other (the radish is Ikar, and the olive is Chaviv), he blesses on each. A Chaviv Tefel gets its own Berachah only if it is eaten by itself. Then, one eats a little first, and then blesses on the Ikar. I prove this from 35a. The Gemara asked when one blesses Borei Peri ha'Etz on olive oil. It suggested that he ingests the oil with bread, but rejected this, for then one blesses only on the bread, for it is Ikar. It gave a weak answer, that he drinks the oil mixed in Anigron. Why didn't it answer that he drinks the oil with bread, and the oil is Chaviv to him? Rather, Chaviv does not help there, for he eats them together.

Note: Perhaps the Gemara did not say that the oil is Chaviv, for most people find pure oil distasteful!

Magen Avraham (3): 'If it is not Chaviv' connotes that even if he likes them equally, he blesses on the olive. What is the reason? The radish is Ikar! Also, one may not cause extra Berachos (215:4)! Also, why did the Gemara suggest that R. Yehudah argues with 'one blesses on the Ikar and exempts the Tefel'? Perhaps he agrees, but just like he holds that when the Tefel is Chaviv, he blesses on it, similarly when the Tefel is one of the seven species! The Beraisa teaches that he blesses on the radish when it is Chaviv! Rather, the Or Zaru'a means that one blesses on the radish only when it is primary and Chaviv. He ate the olive only to blunt the sharpness of the radish. I.e. he felt weak, and primarily wanted to eat the radish, like we say about Peros Ginosar. (Their sweetness causes weakness. One can eat salted food afterwards to revive him from the weakness - Tosfos 44a DH b'Ochlei). If the radish was Ikar but not Chaviv, i.e. he was not weak, even though it seems like the olive is Tefel, the radish is not Ikar, for he eats both together, and he does not prefer the radish. If so, he blesses Borei Peri ha'Etz on the olive, and then Borei Peri ha'Adamah on the radish, for the seven species are preferable, or perhaps in such a case Borei Peri ha'Etz is preferable. Do not say that since we hold that it is better to minimize Berachos, he blesses Borei Peri ha'Adamah on the radish to exempt the olive. One may not do so l'Chatchilah. Also, we hold that bread exempts things that come in a meal, since bread is Ikar, even though presumably the other things are Chaviv. The Rashba brings from the Yerushalmi that one blesses on the Ikar and exempts the Tefel, even if the Tefel is Chaviv.

Gra (DH v'Yesh Omrim): If one blesses on the Tefel when it is Chaviv, all the more so one blesses on the seven species according to R. Yehudah, since he holds that this overrides Chaviv. Tosfos (41a) and R. Yonah (28b DH Mevarech) hold that Chaviv has precedence. However, Chaviv does not help in the Reisha (regarding Ikar and Tefel, to obligate blessing on the Tefel).

Damesek Eliezer: I answer for the Rema that he learns from the Agur, who says that if the olive was Chaviv, he does not bless first on the radish. Perhaps this is only because the olive has two advantages, i.e. it is from the seven species, and it is Chaviv. If a Tefel has only one advantage, i.e. it is Chaviv or from the seven species, one blesses on the Ikar and exempts the Tefel. The Rema comments on the last words of the Mechaber, that even bread can be Tefel. The Rema says that if the Tefel is Chaviv, i.e. regarding bread, which is from the seven species, one blesses on it. Since Rabanan say that one blesses on the radish, we must say that it is not Chaviv. This is unlike Tosfos, who says that Chaviv does not help in the Reisha (to obligate blessing on the olive), even though it is also from the seven species.

Gra: Also, the Rema (211:5) said that ha'Motzi exempts other foods (even if they are Tefel), and here the Mechaber said that bread can be Tefel (and the Rema did not comment).

Damesek Eliezer: The Rema ruled that bread comes before Chaviv. Even so, Ikar overrides bread, even though bread is from the seven species. All the more so Ikar overrides Chaviv, even if the Chaviv is from the seven species.

Mishnah Berurah (6): If one eats cake with cheese or another accompaniment, even if also they are Chaviv to him and he wants to eat them, he blesses only on the cake, for presumably it is Ikar for him. The same applies to anything one eats with another species to accompany it. The accompaniment is only like a Tefel.

Kaf ha'Chayim (5): Because Safek Berachos Lehakel, one should always bless on the Ikar and exempt the Tefel. If they have the same Berachah, all agree that even if the Tefel is Chaviv, he blesses on the Ikar.