matriarchate vs matriarchy

matriarchate and matriarchy both are nouns.

Word	Noun	Adjective	Verb	Adverb
matriarchate	Yes	No	No	No
matriarchy	Yes	No	No	No

As nouns, matriarchate and matriarchy are synonyms defined as:

matriarchate and matriarchy: a form of social organization in which a female is the family head and title is traced through the female line

matriarchate (noun)	matriarchy (noun)
a form of social organization in which a female is the family head and title is traced through the female line	a form of social organization in which a female is the family head and title is traced through the female line