Let us consider a language where no 'adjectives' proper exist. Such languages, by received wisdom, come in two forms: languages that use verbs instead, and languages that use nouns instead.
This dichotomy is somewhat exaggerated in conlang circles, or at least it was about a decade ago or thereabouts. Obviously, pretty much every language has a noun that is pretty much the same as some adjective in another language, and pretty much every language has a verb that is pretty much the same as some simple adjective in another language.
However, let's consider a situation where most of the words an anglophone would think of as adjectives are in fact nouns, so e.g. 'red' is maybe semantically closer to 'a red one' than to 'red'. However, this language permits using nouns in apposition as attributes.
Now, the language has a simple noun class system, maybe four or five classes, and these classes are mainly 'visibly' seen in a fairly small congruence system, with congruence markers appearing on quantifiers, pronouns, demonstratives, articles, and verbs. Thus, the nouns themselves usually do not have a clear class marker (or rather, the morphemes that do appear on nouns may be misleading some of the time, c.f. Latin 'nauta' or Russian 'дядя', both of which end on -a, and "usually" would be feminine, but due to semantics also influencing gender in fact are masculine.
However, nouns used adjectivally need to be of the same noun class. The markers used for 'typecasting' a noun into another noun class, however, have been worn down so that they are all identical, thus the adjectival congruence basically consists of 'no morpheme' = 'same class as head of phrase', 'that morpheme' = 'different class than head of phrase'. Numbers also is part of the class system, but certain nouns are essentially 'plurale tantum' words anyway, and so get 'that morpheme' whenever with a singular noun.
Finally, the genitive in part overlaps with this system: the genitive construction does not use the congruence-marker, being happy enough to just put nouns in apposition. With two nouns of the same noun class, this will be indistinguishable from an "adjectival" noun in apposition to a "nominal" noun.