Final answer:
The constitutional amendment used as the basis for the decision in both Hernandez v. Texas (1954) and Brown v. Board of Education (1954) was the Fourteenth Amendment, which includes the Equal Protection Clause.
Step-by-step explanation:
In the landmark case Hernandez v. Texas (1954), the Fourteenth Amendment of the U.S. Constitution was the constitutional basis for the decision, just as it was in Brown v. Board of Education (1954). The Fourteenth Amendment's Equal Protection Clause was crucial in both cases, as it mandates that no state shall deny any person within its jurisdiction the equal protection of the laws. This provision was used to argue that Mexican Americans in Jackson County, Texas were being discriminated against by being systematically excluded from jury service, and the Supreme Court unanimously agreed that such exclusion was unconstitutional.
The Hernandez v. Texas case was instrumental in extending the protections of the Fourteenth Amendment to all ethnic groups in the United States, reinforcing the principle that the amendment is not limited to a 'two-class theory' of just whites and African Americans but applies to all racial groups.