WASHINGTON--The Supreme Court yesterday heard arguments on the constitutionality of busing school children across school district lines to achieve racial balance.

The case has major implications for the future structure of public educational systems in major cities throughout the nation, including Boston.

The City of Boston has filed an amicus curiae (friend of the court) brief in the case supporting busing across district lines, The Boston Globe reported yesterday.

In question in the suit is whether school children can be transported between Detroit and surrounding suburbs in order to desegregate Detroit schools.

Until the present, the courts have approved busing only within a single school district where violations have occurred. The Detroit plaintiffs argue that the high percentage of black school children in Detroit (65 per cent) precludes the possibility of an integrated system if busing is limited to the city.

Frank Kelley, attorney general of Michigan and counsel for the Michigan State Board of Education, which opposes a metropolitan solution, argued that because only the Detroit School Board, and none of the suburban boards, has been guilty of violations, a remedy for the resulting segregation could not involve suburban districts.

Kelley asserted that the courts must not pursue social goals. He claimed that the pursual of social goals without evidence of violations "tramples" on the rights of local government.

Nicholas Flannery, counsel for the NAACP-supported advocates of trans-district busing, argued that the interaction of residential patterns and school segregation is as important as intentionally discriminatory policies by district school boards.