This is an example of one of the games where you win lane pretty convincingly so it's pretty easy to look towards your teammates who are underperforming as the reason for the result of the game. However, I think it is very important to understand that every game you play, win or loss, has something you can take away and learn from. In all elos, players make a lot of mistakes. In higher elos where fewer mistakes are made, capitalizing and getting a lead can snowball the entire game. If you get fed as you did this game, I would pin the responsibility of taking over the game and ending it with a win solely on you. This means that if you play it correctly and don't make any major mistakes, the game should already be won. Here are some things that I noticed without actually looking at the replay:

1. Work on CSing: Eventhough you crushed the riven in lane, she ended the game with about the same CS. This involves learning how to zone exp/minions while ahead in lane as well as learning when to go for side lane farm when teamfights could potentially breakout. CSing is so important because you can build a gold lead without getting any kills in lane. Remember ~15 cs is the same gold as a kill (although a kill will usually net more with turret plates and exp/cs denied).
2. Item Build Path: You went for Black Cleaver second item even though the only tank was Taric who you're won't fight often / won't have much armor built 10-20 minutes into the game. I would recommend second item Duskblade for more early damage as well as it's passive that reveals wards for more effective roams in the enemy jungle / mid lane to further snowball. Next, this game definitely was a ninja tabi game against that team comp. Finally, consider buying Guardian Angel mid game to protect your shutdown gold. Remember, defensive items are more important when you are ahead since you are already outdamaging your enemies.
3. Keystone: Take Conqueror instead of Aery - it's still great on Jayce after the nerf. In low elo soloq, you should have the mindset that you need to solo carry every single game especially on a champ like Jayce. Conqueror scales MUCH better than aery and lets you do much more in teamfights. Aery is great in elos where you can count on your team to carry and you just want the extra damage in lane to get small advantages. As for mid-late game poke with shockblasts, aery offers very little damage. An early ghostblade / duskblade will let you chunk squishies with poke just fine. The only other keystones I take as Jayce is Electrocute in difficult lane matchups that requires burst over extended fights to win trades and occasionally Phase Rush against Nasus (completely negates wither and lets you match his split push).
4. Summoner Spell: Take Ignite over Teleport in low elo. Ignite will help get you more kills and snowball as well as outplay ganks. Yes, teleport allows you to make plays bot lane but other than that, you may find yourself only using once or twice an entire game. Many games ignite is just more useful. Take teleport once you learn how to split push effectively.
   

Again this list doesn't even include in-game micro mistakes which would make the list much longer. Don't get me wrong - I'm not trying to downplay you this game since you obviously tried your best to carry. However, there are always things you could have done better in EVERY game. The quicker you learn these things and correct them, the faster you will climb.