The graphical representation of a system of two linear equations is two lines. These two lines can
(1) interesct at a point (x, y)
(2) not intersect and be parallel (no solution)
(3) sometimes turn out to be the same line (infinitely many solutions).
These are the only possibilities for a system of two linear equations because when graphed, they will only do these three things.
Please comment with any questions!
