The use of “you” which we understand towards the plural decides the matter; “Your opinion is our interpretation of these words.” Can “you” mean one person, but “both” indicates there are two in this case. Both are my friends, although I would have “Both of you are my friends” rather than “You both,” only because it sounds more natural to my ears than what is required of me. I will be right when I say

both, as a friend do, a friend, as well.