As said in the title, I always duo queue with a friend and our elo's are only 20-30 different, however, we are both always the last two picks during champion selection. When i solo queue im usually towards the top..

Could someone please explain to me why we are always last to pick.

In ranked queue the higher elo players pick first. Technically it's actually a good thing you're at the bottom because it means you're playing with people better than you and if you win your elo will go up more. Also people above you are more likely to carry.

I understand this, however, you would think that every once and a while the matchmaking system would have you and your friend at the top. I'm just curious as at my elo the bot person gets support every time

duo queue has you at an increased elo for matchmaking ( in theory, you can communicate better with your queue partner thus gain an unfair advantage against people of your elo, so you're set to fight against people of higher elo ) but in champion select you are set according to your own elo, thus you're the last picks

Thankyou heaps, it makes sense when you put it like this and I understand now.