Unless you a smurfing, there is no getting out of bronze (let alone bronze 4) with a "solo carry" mentality. I mean, it is possible, its just really really hard and there are easier ways to go about it.
Teamwork is a massive part of this, and if you are going into a game with the expectation of a potato team, you aren't going to be playing your best. You are also more likely to flame, which in turn makes everyone else play worse. The ranked system is fine, you get matches with people who are generally your own skill level.
Own your mistakes and learn from them! This is how you will climb.
In general, to climb:
Join a premade team
Bronze IV is the ultimate cesspit for trolls and people who play like bots. Playing ranked is like dipping your hand into medical waste and hoping you don't get hepatitis. Playing as a ranked 5 will definitely lessen your chances of being matched with trollers/afks/other toxins. It also allows you to become familiar with the play patterns of your teammates (so you don't have to keep adjusting your style every game) and you have way better communication. With the implementation of a dynamic queue where this is possible, there is literally no reason not to. You also get lots of cool bonuses like extra IP, mastery points and Hextech stuff (soon™).
Play comfort picks rather than counter picks.
A lot of people in bronze get caught up in trying to play counter picks, even if they have no idea how to play the champion. Same happens when the "FOTM OP" isn't banned. A lot of people are going to be playing "op" champs in order to get out, and the likelihood of them sucking is high (look at all the bronze v vaynes and yasuos). Playing a comfort pick means that you will not only have better matchup and skill knowledge, it means that you have more options on how you want to play (aggro/safe/roam). Keep in mind that your comfort picks may be banned, I would suggest picking up a couple of champs (also helpful if you are last pick and your team is missing something like a tank).
3. Get super good at two roles.
Dynamic queue allows you to choose two roles, so you have 100% chance of getting of your fave/best roles. Pick up a few comfort champs in each, learn all there is to know about them so you know things like build paths and matchups like the back of your hand.
_Note: I would suggest picking 3 champs for each role you want to play. Pick an AD, an AP, and a tank so that you are able to fill what your team needs. Playing Raka every single game isn't going to work all the time. _
For support: Raka (utility), Annie (AP), Leo/tahm (tank)
For top: Cho (AP tank), Irelia (AD tank), Mundo (tank)
4. Revisit some of the basic league skills.
Things like CS, warding, positioning, teamcomps, and being a nice person and encouraging your team. If you need help with some of this, you could consider hiring a coach.
Note: also check your masteries and rune pages are the best they can be.
**5. Keep a ranked diary. **
Most of my improvement comes from my ranked diary. After every game I write down who I was playing, my score, CS, wards placed, LP gained/lost and a quick summary of the game. I also like to write down 3 things I did well, and 3 things I need to improve. That way, you are really processing the game and learning from your mistakes. It also gives you something to consciously work towards improving in the next game.
TL:DR, Improve yourself. You perform worse than the average player in almost all respects, and I can tell you now, that isn't your teams fault.
Good luck, may the elo be ever in your favour ♥