I would never normally advocate deleting your LinkedIn account! LinkedIn is the most important network – the one you should choose if you had to choose one.
But I have noticed that sometimes, you search for someone and 2 versions of them popup on LinkedIn! Confusing, and messy! We don’t want that, we want to clean up the internet!
The main thing is to have your username and password handy for each of your LinkedIn accounts.
You may need to use “forgot password”
Then you login to the one you don’t want.
Make sure that if there is anything you want to keep, eg some good descriptions of your current and previous roles, or dates where you worked at different places, you copy paste that into a spare file and save it safely for use later (on your proper LinkedIn profile). Also make a note of the contacts you may have on this one you want to delete so you can connect with them again on your other “proper” LinkedIn profile.
You go to the top right corner where there is a thumbnail which would be a profile picture – and if there isn’t a profile picture, it will be a little silhouette – and choose “Privacy and Settings”

 
Then click on Account and choose “Close your account”

Choose a reason and click continue

Confirm and delete!
 
(but only do this on the account you really want to delete!)