Use the singular ( value system ), which is the usual form when using nouns as attributive modifiers: shoe store, pencil case , etc. By the way, your dictionary definition is misleading, since the use of plural 'values' is no different than it is for any other countable noun. You can discuss 'family values' or just a single 'family value', just as you can have 'two shirts' or 'one shirt'.
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Your dictionary is correct. Values in the sense of traditional values is always plural.
You would say "values system". You cannot say "one traditional value" or "family is a traditional value" because values is always plural and uncountable. You have to rephrase as "family is one of american traditional values". Some people will say "family is a traditional values" which is better tha