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The fate of Michigan's voter-approved ban on same-sex marriage will be decided within two weeks, the federal judge hearing a lawsuit by a same-sex couple said Friday.

Closing arguments in U.S. District Court in Detroit centered on the credibility of academic studies examining whether children raised by same-sex couples are worse off.

Jayne Rowse and April DeBoer, a lesbian couple from Hazel Park in the suburbs of Detroit, are seeking to overturn a constitutional amendment voters passed in 2004 to define marriage as being between a man and a woman. They say they want to legally adopt the three children they've been raising but can't because they're not legally married.

Plaintiffs April DeBoer, left, and her partner, Jayne Rowse, leave U.S. District Court in Detroit on Friday with their attorney, Dana Nessel.Rebecca Cook / REUTERS

"We're not numbers. We're not a number," Rowse told NBC station WDIV of Detroit. "We're just one family in the big pool that's here fighting for our kids' rights. That's all we're here for. That's all we have been here for."

U.S. District Judge Bernard Friedman said that final briefs were due Monday and that he expected to issue a ruling within two weeks. If he overturns the amendment, Michigan would become the 18th state to legalize same-sex marriage.

Lawyers for Rowse and DeBoer sought to undermine the state's final scientific witnesses Wednesday and Thursday.

The Oakland County Clerk's Office said that if Friedman overturns the ban, it will begin issuing marriage licenses to same-sex couples immediately.