System of equations with multiple intersection points

Hi, I was just wondering what happens when you've got a system of equations and multiple intersection points happen from those lines? For example:

http://i39.tinypic.com/eqts2q.gif

There seems to be more than 1 point between the two lines that intersect with each other. I am guessing that the system will solve into something that has a sort of equation for the Y variable? Such as: (x, 2x+1) ? And if I'm correct with that assumption, is there a way to find an interval for the range of valid x values?