delete user account

Hi Folks thanks for all the previous sound advice!
Here is another problem to solve
I purchased a Mac 2009 from a previous owner now updated to Yosemite however there is still there user account listed that I cannot delete they did supply me with their password when they set it up initially they purchased it for a business venture that never took off and had little use of Mac with not a lot of programmes installed which I have deleted with any other files I can find but need to delete their user account
All suggestions greatly appreciated
Cheers
ben

Create a second admin account from the Users & Groups System Preference. Unlock if needed.
Turn off automatic logins under Login Options.
Reboot the Mac
Login as the new admin user you just created
Open the Users & Groups System Preference and unlock it if needed.
Use the minus sign button to delete the unwanted account. You will be presented three options. Leave the home folder alone, create a disk image from the home folder or delete the home folder.

Do yourself a favor. When you buy a computer from someone else, wipe the drive and reinstall the system.
This assures there is nothing on there you don't want and removes any other user accounts.
Zod knows what kind of stuff they had running on there.
If you don't have an install media re-download Yosemite and create an install USB stick.
There are instructions all over the web on how to do this.

+1 for cradom's suggestion. Did you do the updating to Yosemite? If not security and other updates will not be available to you, only the person's Apple ID which downloaded Yosemite.