Riot, this is a Behavior question

Last night I was in a game with two children arguing with each other, me and the other team mates were trying to convince one of them to mute each other.

They BOTH didn't want to mute each other, instead they continued to argue throughout the game to a point where we lost the game due to one of them saying " I'm throwing this game then AFK'ing "

Obviously the solution to this is to Report them but this isn't the case, I've encountered these behaviors more than 10 times in the last month (I'm sure of it) I chose not to mute either of them because sometimes I'm able to convince one of them. I don't like losing Rank games, I don't like losing so much LP for these kinds of things and I don't like being in a team with people who still roam around the game with that kind of attitude.

So if you were in my Shoes, how would you resort to this problem?