How do reports work?

you press the report button and the player gets reported

Reports flag a game for review. The system then checks the chat (most common instance) for toxicity and takes appropriate action

As Avatel said, reports only flag a game for review. That means that even if you convinced all 9 other players to report someone, they may not be punished.

There is an automated system for toxicity but I believe based on the player's punishment level, a Riot member will also come in to see if what they said was ban worthy.