Without using a database you would be forced to use an array,
I would suggest an array within an array, so you in fact are using 3 arrays in total. 1 your main array, 2, your Username array 3, your corresponding Password array.
To make sure they login, requires the use of sessions. Session variables throughout your site can help ensure that the user logged in has access to whatever you designate him / her to look at.
I hope this helps, if you require consultation on this in any further depth please feel free to contact me.