במדבר פרק לג, ג
ג וַיִּסְעוּ מֵרַעְמְסֵס בַּחֹדֶשׁ הָרִאשׁוֹן בַּחֲמִשָּׁה עָשָׂר יוֹם לַחֹדֶשׁ הָרִאשׁוֹן מִמָּחֳרַת הַפֶּסַח יָצְאוּ בְנֵי-יִשְׂרָאֵל בְּיָד רָמָה לְעֵינֵי כָּל-מִצְרָיִם:
The verse implies that the “day after” Pesach means the day after the offering of the Korban Pesach (14th of Nissan), thus, the “day after” referred to in the verse means the 15th of Nissan, even though that day is Yom Tov. Need to remember that in the year of the Exodus from Egypt, the night of the 15th was not subject to the concept of guarding of Yom Tov. Further, regarding Korbanos, the night follows the day. Therefore, the command to eat the Pesach at the night of 15th of Nissan was connected to the day of the 14th. Therefore, both the day of the 14th and the night of the 15th are called Chag haPesach.
According to the Torah, the day of the 14th is called Chag haPesach, but is not called Chag haMatzos. However, the Rabbis did call the day of the 14th Chag haMatzos (Pesachim 13b).
And this provides a support to the Rema (Y.D. 399) that states that no mourning is allowed on Erev Pesach (the 14th). The Shach questions this law. However, the support of the Rema is that Erev Pesach is called a double-named holiday, Chag haPesach and Chag haMatzos.
במדבר פרק לה, כד וּשְׁפָטוּ הָעֵדָה וְהִצִּילוּ הָעֵדָה
It is known that the word עדה refers to the Sanhedrin. The Sanhedrin should judge and attempt to find merit for the defendants (להציל to save them). Thus, the court that executes once in seven years is called a destructive court.
The term עדה refers to a set group of judges, rather than a group of people, meaning a group gathered just for each case. It could not be that a random gathering of people should have the knowledge and capability to properly judge.
Further, VaYikra (4, 13) refers to the accidental wrong of the עדת ישראל, which can not refer to the entire Jewish nation, since that would be impossible for everyone to do such an unintentional act. Rather, Chaz’’al say this refers to the Sanhedrin who are not angels and yet have a possibility of committing errors.
The word Sanhedrin is from a Roman word (similar to the English word Senate), which indicates a gathering of highly selected individuals. Thus, originally Moshe gathered 70 elders with himself as the head into a specialized group.
Therefore, the word עדה can signify a gathering of selected individuals from the root word יעד (appointed), and thus, עדה can mean the Sanhedrin.
Further, the Hebrew word סנהדרין is treated like a feminine word (סנהדרין גדדולה, סנהדרין קטנה), since the source of the word is identified with כניסה או עדה.