282
Opinion of the Court
least as alternative grounds for their decisions, see 463 U. S., at 591-592 (opinion of White, J.); id., at 623, n. 15 (Marshall, J., dissenting); id., at 643-645 (Stevens, J., joined by Brennan and Blackmun, JJ., dissenting), and dictum in Alexander v. Choate is to the same effect, see 469 U. S., at 293, 295, n. 11. These statements are in considerable tension with the rule of Bakke and Guardians that § 601 forbids only intentional discrimination, see, e. g., Guardians Assn. v. Civil Serv. Comm'n of New York City, supra, at 612-613 (O'Connor, J., concurring in judgment), but petitioners have not challenged the regulations here. We therefore assume for the purposes of deciding this case that the DOJ and DOT regulations proscribing activities that have a disparate impact on the basis of race are valid.
Respondents assert that the issue in this case, like the first two described above, has been resolved by our cases. To reject a private cause of action to enforce the disparate-impact regulations, they say, we would "[have] to ignore the actual language of Guardians and Cannon." Brief for Respondents 13. The language in Cannon to which respondents refer does not in fact support their position, as we shall discuss at length below, see infra, at 288-290. But in any event, this Court is bound by holdings, not language. Cannon was decided on the assumption that the University of Chicago had intentionally discriminated against petitioner. See 441 U. S., at 680 (noting that respondents "admitted arguendo" that petitioner's "applications for admission to medical school were denied by the respondents because she is a woman"). It therefore held that Title IX created a private right of action to enforce its ban on intentional discrimination, but had no occasion to consider whether the right reached regulations barring disparate-impact discrimination.2 In Guardians, the Court held that private individu-2 Although the dissent acknowledges that "the breadth of [Cannon's] precedent is a matter upon which reasonable jurists may differ," post, at 313, it disagrees with our reading of Cannon's holding because it thinks
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