Is it possible for a son and his mother to offer one seventh of a big sacrificial calf as an Udh’hiyah that is shared by seven people? The son has a job and he lives with his mother.
All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
It is narrated on the authority of ‘Ataa’ ibn Yasaar that he said, “I asked Abu Ayyoob, ‘How was the Udh’hiyah done at the time of the Messenger of Allah ?’ He said, ‘A man would offer a sheep on behalf of himself and the members of his household, and they would eat some and feed others with some, until people began boasting, and the situation now is as you see.’” [Ibn Maajah, At-Tirmithi: Saheeh]
This Hadeeth is an evident proof that people living in the same house can sacrifice one sheep or one seventh of a camel or a cow. It is narrated on the authority of Jaabir ibn ‘Abdullaah, may Allah be pleased with him, that he said, “We set out with the Messenger of Allah for Hajj. He commanded that we share camels and cows, and each seven of us share an animal.” [Muslim]
Thus, if that son and his mother live in the same house in such a way that they can truly be called members of the same household and they share the same source of provision, then one seventh of a cow will suffice them.
It should be noted that the cow must be two years old or more, because the Messenger said: “Do not slaughter but a Musinnah (a two year old cow or a five year old camel or a one year old sheep).” [Muslim]
Allah Knows best.