"I read, you write."
Translation:Io leggo, tu scrivi.
Technically, yes. You can say "leggo, scrivi" and be understood, because the verbs are conjugated to imply who reads, and who writes. Further, you could simply write "Leggo." and this would be grammatically and semantically correct. Obviously you could do the same with "scrivi". Think about it: "you write/you are writing" is a perfectly acceptable sentence in English and is the direct translation.
Italian is what is known as a "pro-drop" language which means, as Jess mentioned, that the pronoun can be omitted because conjugated verbs conform to the first, second and third person.
As for the sentence being "awkward," I agree it does sound a bit abrupt. You wouldn't really use it in conversation unless you wanted to send someone on their way.
As I understand it, the subject pronoun (io, tu etc) can always be omitted if it is clear from the verb or from the context who is the subject of the verb. In this case the verb endings makes it perfectly clear who is the subject of each verb, so omission of io and tu is fine.
(Duolingo accepted "leggo, scrivi" when I put it in)
Uh...no. It says "you write" not indicating whether it is plural or not. So then "voi" should be correct or not?
VOI also can mean YOU (singular) for informal but is not used anymore as we now use only LEI (You, singular, formal) except if you are talking with the King or the Pope: sua Maestà, voi siete molto... =her majesty, you are... sua santità, voi siete... =(her?) santity, you are...
I answered: "Leggo, scrivete" which should also be right. 'You write" could also be plural, but duolingo marked it as a mistake. I know "you" in its plural form is usually indicated as "you all", but technically my answer should not be a mistake. Missed some lingotto's because of this ;-)
I am guessing the you are doing as so many of us did when starting out within Duolingo and not realising that it is nothing that 'you' are doing wrong. It is in fact the fault of the Type Font that Duolingo has chosen that causes the issue and there for our seemingly incorrect answers.
When using 'io' it most often looks in the reading matter like 'lo'; Lower case 'i' and lower case 'l' being the main culprits.
Try using 'i' instead of 'l' in place of what you have been using in instances of it otherwise being the correct answer.
For example: io sono, Io sono These are both with the letter 'i' for indigo and not the letter 'l' for lima.
Hope this helps and let me know how you go on, good luck!