Answer:
They attempted to keep their schools segregated.
Step-by-step explanation:
The Brown v. Board of Education of Topeka was a landmark litigation or court case between Oliver Brown and the Board of Education in which the justices of the Supreme Court unanimously ruled (9-0) in 1954 that racially segregating children in public schools was unconstitutional because it violates the Equal Protection Clause of the Fourteenth Amendment (14th) of the Constitution of the United States of America.
Meanwhile, on the 4th of September, 1957, the first day of resumption of class activities at Central High School, the Governor of Arkansas, Orval Eugene Faubus invited the Arkansas National Guard to block all African-Americans (black) students from entering into the school.
Hence, the states with segregated school systems responded to the Supreme Court ruling in Brown v. Board of Education by attempting to keep their schools segregated.