(a) The county board of education in each county shall consist of five members elected by the voters of the county at large for terms of four years: Provided, that where there are multiple local school administrative units located within the county, and unless the county board is responsible for appointing members of the board of education of a city administrative unit located within the county, only those voters who reside within the county school administrative unit boundary lines shall be eligible to vote for members of the county board of education. Where the county board is responsible for appointing members of the board of education of a city administrative unit located within the county, the voters residing within that city school administrative unit shall be eligible to vote for members of the county board of education. The terms of office of the members of boards of education of all school administrative units in this State, who serve on June 25, 1975, shall continue until members are elected and qualified as provided in this section unless modified by local legislation.