The only way to 'carry' a game is to completely and utterly destroy your lane opponent so badly that you can 1v2 him and the enemy jungler, when the jungler comes to camp you. That's when you truly won your lane (or when you can just kill him over and over and force him to leave it).
Then assuming your team DID NOT feed as hard as YOU got fed yourself, by grouping, warding the jungles, warding objectives and destroying the enemy team in outplays and teamfights, and making sure you keep pinging, that's basically how you carry a game. And USUALLY you should be able to win these games more than your team throws (thus, if you destroyed your lane 90% of your games, you WILL gain elo).
Now, if you just go even lane or have a small advantage (CS, 1 kill ,etc), then no, you can't "hard carry"--you are going to be reliant on teamwork and getting people to cooperate and make smart plays. If they don't do that, then you had better hope the enemy team throws harder than you guys are. Or you lose.