How does y=2x-2 have infinite number of solutions

This has infinite solutions because x + x - 2 = 2x - 2

It does not  matter what number x is

If you think about it this way,

Y and X could mean ANYTHING just as long as they are equal to each other.

For example: let x = 2, so 2x-2 =2
Well...set y=2, and there you have it! 

Another one: let x = 3, so 2x-2 = 3
Wellset y = 3hopefully you get the idea.

Once againsince there are two variables are in one equation, and that equation is not in a system, ANY two values for X and Y will equal the same, but they HAVE  to equal.

Hope this helps. :)