A function is a collection of ordered pairs (x,y) where for any x in the domain, there is only y paired with it. A graph is a convenient way to visualize the (x,y) pairs as coordinates in 2 dimensional plane.

If the graphs of two functions intersect, then they must share some pair (x,y) in common. In you example, equation 1 is the set of points (x, x+1) and equation 2 is the set of points (x,2x-1). If those two graphs intersect, then there must be some point (x,y) shared by both. Let’s assume that happens when x=a. Then the point is represented as (a,a+1) on the first graph and (a,2a-1) on the second graph. But if they are the same point, then the x and y coordinates must be equal. Setting the x values equal gives a = a, which isn’t very interesting. But setting the y values equal gives a+1 = 2a-1, from which get a=2. Plugging that into either equation gives a y value of 3. So, the graphs intersect at (2,3) because the point (2,3) is on both graphs. Typically, we just skip the part where we say that x=a and just work directly with the variables c and y.