"If we had met when we were young, life would be very different."
Translation:Eğer gençken seninle karşılaşsaydık hayat çok farklı olurdu.
It's very common in Turkish to conjugate the verb for "we" when there is a "with you" present in the sentence.
I went there with you. = "Oraya seninle gittim." OR "Oraya seninle gittik."
I spoke to you. = "Seninle konuştum." OR "Seninle konuştuk."
It's like, "with you" as in "you and I", which makes it "we".
Of course this could create ambiguities, as in, perhaps me and a few other people did the action with you, so it's not just "you and I", but well… it's not such an important detail ;p It's usually understood from the context. And if you don't want to talk like that, you can always use the 1st person conjugation; there is nothing wrong with that.
This was very helpful for me. And here are all cases very good explained.