It's a myth that every game is carryable, and it's a myth that supports cannot carry games. If you're soloqueueing, your best bet is to go as a "support" like Brand or Annie and just murder everything yourself. If you're playing with someone you trust or you hit the level of play where carries are capable of right clicking on things, you can play defensive supports and just protect them all day every day and set them up for easy kills and win that way.
This, so much. Supports can carry just as well as any other role, the important point is always that you play a champion and a role that you're confident with.
In particular, if you've got some awareness of how to counter-pick, that alone can carry you in lower divisions. I duo'd in normals with someone I know yesterday. I picked Top/Fill and ended up playing Support. My ADC was Bronze III Mid main, my Mid was a level 25, my Top was Bronze III, and my buddy on Jungle TF was Bronze IV. I was Silver I with mid-high Gold ELO when I quit playing ranked back in S4.
On the other team, this is what they had:
Top: Bronze III
Jung: Bronze V
Mid: Silver IV
ADC: Level 10
Supp: Unranked, 1 loss in S4, 24 games played and a 58% loss rate in S3.
So it was basically as Bronze as you get, short of a true Wood League full Bronze V match. One player on each team wasn't even at level 30. Their one Silver was playing Yasuo mid (an easy carry position, laning against a player below level 30), while our one Silver was playing Support. As soon as they locked Sona I picked Leona. I told Varus to hard-push, and as soon as we hit level 2 I all-inned Sona, giving him the kill. At around 5:30 we shoved all the way into tower and dove; I picked up a double and moved into their Gromp brush to recall. TF had chased Voli into the river brush and the latter flashed over the wall; I was almost dead but outplayed and secured the triple. A bit later, I brought Varus to mid, we shoved Yasuo out of lane and forced the tower.
Over the while or so, Yasuo got pretty fed. I started farming (in part because barely anyone on my team bothered to clear lanes) and itemized against him. Every teamfight was shit, people got caught constantly, but I focused on waveclear and killing Yasuo. They ran it back really heavily up until I got a good engage at Baron and we Aced them. A few minutes later, Yasuo misplayed, I caught him, and Kayle was fed enough to clean house.
Here's the match.That's pretty representative of the different ways of carrying in low ELO as support. First: do it yourself. Bully the enemy laners early, go for kills if you can snag them. If you're playing a high-damage support like frost mentioned, keep doing that. If you're playing a tanky support, become unkillable and hope that you have a competent carry (if you do, follow them around and protect them from their own mistakes while setting up kills for them). If you're playing a utility support in low ELO you're fucking dumb. The bottom line is that, like any other role, you have to be a forklift or a dump truck. Either you lift your team up and shove them at the enemy, cleaning up in their wake, or you load them all into your backpack and drive them to victory, come hell or high water.
Don't bother being a team player unless you have a teammate worth playing with. If you do, do what I did with Kayle and give them everything you can. If you don't, focus on waveclear and objectives. The latter is the main reasoning behind the "supports can't carry" myth: many supports don't have good waveclear or objective-taking potential, which means that they're more reliant on having a good teammate to play off of. If you're doing well, don't refrain from farming if nobody else is around to take the CS. Don't be afraid of taking kills either. You might get flamed, but you'll get flamed just as much if the wave pushes into tower, a teammate gets killed shoving it out too far, or a kill escapes because you're playing with braindead morons who can't secure a sure thing.