One way of thinking about this problem is that we are looking for the intersection of two equations:

1. y=x+2/3

2. y=4/x+1

The first equation is a straight line:

The second equation is a hyperbola:

If we overlay the two equations, we can see where they intersect:

If we rearrange the terms, we can restate the equation as follows: 3x²-x-12=0. This describes a parabola:

The points of intersection are as follows: