When we sit down to the seder, among the most important mitzvot that we fulfill is eating matza and maror. Our tradition is to first make the appropriate blessings (ha-motzi and al akhilat matza) on the matza, then to make the blessing on the maror (al akhilat maror – the blessing of borei pri ha-adama having already been recited on the karpas), and finally to make a sandwich from them together, reminding us of Hillel’s tradition during Temple times.
This tradition is based on the conclusion of the Gemara in Massekhet Pesaḥim (115a), which points out that Hillel was of the opinion that ein mitzvot mevatlot zo et zo – that two mitzvot done together do not nullify one-another. That is to say, that the commandment to eat matza (or maror) does not need to be done on its own and can be done in conjunction with another commandment. Hillel argues that this is the intention of the passage (Bamidbar 9:11) al matzot u-merarim yokhluhu – that the Passover sacrifice will be eaten together with the matza and the maror.
Although our Gemara attributes the idea of ein mitzvot mevatlot zo et zo to Hillel, the conclusion of the Gemara in Pesaḥim is that the rest of the Sages essentially agree to that principle; their argument is that it is not necessary to eat the matza and maror that way.
The Talmud Yerushalmi disagrees and suggests that although the Sages who argue with Hillel believe that two mitzvot will not negate each other, if there are three mitzvot being done at the same time, then two mitzvot will overwhelm the third mitzva.
Another point of difference between our Gemara and the Yerushalmi relates to mitzvot that are obligatory on different levels. According to our Gemara, mitzvot do not negate each other only if both of the commandments being fulfilled at the same time are on the same level – that they are both Biblical commands. If, however, one of them was on a lower level (i.e., if one of them was only a Rabbinic obligation), then we would rule that they could not be done together. Since the accepted halakha is that since the destruction of the Temple – with the korban Pesaḥ no longer being sacrificed – maror is only a Rabbinic obligation, we can no longer eat matza and maror together. Thus we first eat them separately and only afterwards eat them together as a remembrance of what Hillel did in the time of the Mikdash.
According to the Yerushalmi no one suggests that a Rabbinic commandment can negate a Biblical one; the only disagreement relates to Biblical commandments that overlap one-another.