Short Answer 
The Supreme Court cases Regents of the University of California v. Bakke and United States v. Virginia significantly influenced educational policies on affirmative action and gender equality. Bakke established that while strict racial quotas are unconstitutional, race can still be a factor in admissions, whereas the Virginia case mandated that gender-based exclusions in education are impermissible, promoting equal opportunities for all genders.
Step 1: Understanding Important Supreme Court Cases
The cases of Regents of the University of California v. Bakke (1978) and United States v. Virginia (1996) are pivotal in shaping educational policies and affirmative action. The Bakke case addressed the constitutionality of racial quotas in college admissions, leading to a ruling that allowed race to be considered but not as a strict quota. This case established a foundation for how race could be used in admissions without discrimination against other applicants.
Step 2: Bakke vs. Quotas
Allan Bakke’s challenge to the UC Davis Medical School admissions process highlighted the tension between affirmative action and individual rights. The Supreme Court’s ruling was crucial in affirming that:
- Strict racial quotas are unconstitutional.
- Race can still be a factor among multiple criteria in the admissions process.
- Fair treatment in admissions should be prioritized to avoid discrimination.
Step 3: The Shift Toward Gender Equality
The United States v. Virginia decision represented a significant shift towards gender equality in education. This ruling mandated that:
- The Virginia Military Institute must accept women, dismantling its male-only policy.
- Gender-based exclusions violate equal protection under the law.
- Educational institutions must provide equal opportunities regardless of gender.