In sociology, what is the term for a social system in which power and authority are vested in the eldest male member of the family?

The term for a social system in which power and authority are vested in the eldest male member of the family in sociology is called "Patriarchy".

Here are the steps to understand this:

1. Sociology is the study of society, patterns of social relationships, social interaction, and culture that surrounds everyday life.

2. A social system is an interdependent set of cultural and structural elements that can be thought of as a unit.

3. Power and authority vested in the eldest male member of the family means that the oldest man in the family has the final say in decision making and has a dominant role.

4. This type of social system is known as a "Patriarchy". It is a system where men hold primary power and predominate in roles of political leadership, moral authority, social privilege, and control of property. In the domain of the family, fathers or father-figures hold authority over women and children.