Is Solo Queue Impossible to Carry?

The short answer is no. Solo queue is in fact quite easy to "carry." Just remember that you can't win them all, but you can win most of them if you put your heart to it!
*I do not advice duo queue for 2 reasons
1) You're too comfortable and make more mistakes than if you go in a ranked game alone.
2) Your team will be lower ranking in comparison to the other team to compensate the duo queue, which means you'll have even more "scrub teammates."
Just avoid duo queue for ranked if you really want to begin your ELO climb adventures.
Step 1: Champ Select
Be prepared to fill. If you feel you're way better at a role than every other role, than just call that role when you enter champion select. If you don't get that role(s), then just play whatever is left. If other people are arguing over a role, and you're caught with a double jungle or an "afk" or "feed" in champion select, then just dodge. If you're really stingy about that 3 lp, if you already dodged, or if you're in promos, then…
*I do not advice duo queue for 2 reasons
1) You're too comfortable and make more mistakes than if you go in a ranked game alone.
2) Your team will be lower ranking in comparison to the other team to compensate the duo queue, which means you'll have even more "scrub teammates."
Just avoid duo queue for ranked if you really want to begin your ELO climb adventures.
Step 1: Champ Select
Be prepared to fill. If you feel you're way better at a role than every other role, than just call that role when you enter champion select. If you don't get that role(s), then just play whatever is left. If other people are arguing over a role, and you're caught with a double jungle or an "afk" or "feed" in champion select, then just dodge. If you're really stingy about that 3 lp, if you already dodged, or if you're in promos, then…