Does the sacrificial animal of Hajj suffice for the 'Id sacrifice?

Question:
The questioner says, "O honorable Shaykh: I intend to perform Hajj in the tamattu' manner next year, if Allah wills. But if I want to offer a sacrifice on behalf of myself and my family, will the sacrificial animal of Hajj suffice?"

Answer:
The hady is not the udhiyah. May Allah reward you. The hady is one thing, and the udhiyah is another. The hady is for tamattu', while the udhiyah is recommended for everyone, even if they do not perform Hajj. It is recommended for all people, whether they live in cities or the desert, in villages or towns. One udhiyah suffices for a man and his household.
The Messenger of Allah (peace and blessings be upon him) used to sacrifice two rams on behalf of himself, his household, and the Ummah of Muhammad (peace and blessings be upon him). Every year he would sacrifice two rams, black with white markings and having horns: one he would slaughter for himself and his household, and the other for whoever among his Ummah had declared the oneness of Allah, peace and blessings be upon him.
So the Sunnah for you, O Abdullah, is to sacrifice one animal on behalf of yourself and your household: your wife, your children, and your parents. If you sacrifice two or three, there is nothing wrong with it. Do not leave it off if you are able. But if you are unable: [Surat al-Taghabun:16], but with the ability, it is a Sunnah, not obligatory, but it is a Sunnah.