"Eres casado" is an adjective which is often translated as "you're married", and "soltero" is an adjective which is often translated as "single". Learn more about the difference between "eres casado" and "soltero" below.
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el soltero, la soltera
This means that the noun can be masculine or feminine, depending on the gender of person it refers to (e.g. el doctor, la doctora).