Two systems on one iMac - how do I delete one?

Our last Mac died and we bought an iMac early last year which came with Lion/Mountain Lion already installed.  I then installed Mavericks this year.
I had backed up our old mac and managed to transfer the files to the new iMac but I seem to have both Snow Leopard (backed up files) and Mountain Lion/Mavericks running independently.  I can log out of one and then log into the other which I did to ensure all - or at least - most of my files were available in Mountain Lion.
I have all the files I need and the computer just seems to be running so slowly so is it possible to now delete Snow Leopard?  Will it make my mac any faster and will I lose everything I already have?
I am sorry to be such a fool but I really don't understand how computers work and my husband is much better at woodwork!
Please can someone help me?
Thank you.
Corky's mum!

What do you mean by deleting the account? One can't delete an Apple ID/iTunes account. One just stops using it.
Since yo can only have five computer authorized for one iTunes account you might want to deauthorize the computer for that account
iTunes Store: About authorization and deauthorization

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