Here are two views about how to symbolically represent two linear functions plotted in the {x,y} plane.
1) A pair of simultaneous linear equations of the form ax + by = c and Ax + By = C, or
2) A single equation of the form px + q = Px + Q.
If you regard the two linear functions as a pair of simultaneous linear equations then the solution set is the point in the {x,y} plane where the graphs of ax + by = c and Ax + By = C intersect.
If you regard the two linear functions as a single equation of the form ax + by = c and Ax + By =C then the solution set is the point on the x axis whose x coordinate is the x coordinate of the intersection point of the two graphs.
Which formulation do you prefer ? Why ?
What problems could/would you pose to your students based on this applet ?