Class I school districts which have voted to have a six-member school board pursuant to section 79-548 may elect the board members at the statewide primary election. The members of the school board serving when it is decided to elect at the statewide primary election shall continue in office until the first Tuesday in June following the next statewide primary election, at which election a six-member board shall be elected. The three members receiving the highest number of votes shall be elected for terms of four years, and the three members receiving the next highest number of votes shall be elected for terms of two years. Each member's term of office shall begin on the first Tuesday in June following his or her election and, except as otherwise provided in this section, shall continue for four years or until the member's successor is elected and qualified. The members shall meet the qualifications found in section 79-543.