Gay couples began marrying in Miami on Monday, kicking off a pivotal week when the Supreme Court will have a chance to consider whether same-sex couples have a constitutional right to marry or whether states may limit marriage to a man and a woman.

A Miami-Dade County judge gave couples there a head start before marriages begin elsewhere Tuesday in the nation’s third-most-populous state. With the addition of Florida, more than 70 percent of Americans now live in the 36 states and the District of Columbia where same-sex marriages are allowed, according to estimates by the Williams Institute at the UCLA School of Law.

On Friday, Supreme Court justices will meet in private to consider whether to act on cases that could provide a nationwide answer on whether same-sex marriages must be allowed. On the same day, a federal appeals court will consider bans in Texas, Mississippi and Louisiana.