Is "responsum est dilectio" the correct translation for "love is the answer"? The translation comes from Google Translate, but I can't find any proof or usage of the sentence which kind of makes me a bit skeptic.
Latin tends to be more concrete than English, and there is no really satisfying substantive for "answer." I would therefore recast this sentence with a verb.
One option, reminiscent of the popular phrase "omnia vincit amor," is:
Omnia explicat amor.
Explico literally means "unwrinkle" or "unfold," but its (common) extended meaning, according to L&S, is "to disentangle, set in order, arrange, regulate, settle, adjust any thing complicated or difficult."
Unfortunately, Google Translate is notoriously bad at Latin. But in this case it came fairly close. That phrase is grammatically correct and means something like "the response is affection".
For a proper translation, it depends what you mean by "love".
The most standard word for love is amor, as in amor omnia vincit "love conquers all" (Vergil). This traditionally refers to romantic love, but not always: the word for "friendship", amicitia, comes from the same root.
Another potential word is the one Google chose, dilectio. This literally means "choosing" or "favoring", and is more commonly translated as "affection". It's more common than amor for love between family members, as in o luci magis dilecta sorori "you [are] more beloved to your sister than life itself" (Vergil).
The third option is the more Christian one, caritas, usually translated as "caring". This is the one used in I John 4:8, qui non diligit non novit Deum quoniam Deus caritas est "he who does not love does not know God, for God is love" (Vulgate). (Notably, the verb used for "love" here is related to dilectio instead.)
As far as "answer" goes, responsum is a literal answer (as in the thing you say when someone asks you a question). An exitus is literally a departure or exit, but can also mean the solution to something difficult. And an explicatio is literally an unfolding or uncoiling, but can also mean an explanation or solution to a problem.
Whichever you choose, the simplest phrasing is [love] est [answer], [love] [answer] est, or even just [love] [answer]. (In mottos especially it's common to leave out forms of "to be" for brevity.)
So putting it all together, my preference would be for caritas explicatio est. Literally, "caring is the solution".