"Esztergom and Budapest lie beside a river."
Translation:Esztergom és Budapest folyó mellett fekszik.
Because all the nouns in the subject are in the singular.
Hungarian likes to keep things singular if it can get away with it :)
It's possible to use a plural verb as well in such a case, but I gather that this is a recent innovation based on western European languages.
In English, to keep the verb singular, you'd have to say "subject A and subject B each singular-verb." Otherwise, the plural. Maybe "each" is sort of implied in Hungarian?
I presume there is no "egy" before "folyó" because Esztergom and Budapest are on different rivers.