Intersecting lines have one point in common. The solution of the two equations (or the system of equation), is the point where both graphs intersect
Parallel lines have no solutions in common
Similar lines have infinite solution. After plotting both graphs, the tends to overlap each other and look like a single line
(1) y = 4x + 1, y = x - 2 ( 2) -6x + y = 4, -y -2x = 4 (3) x - 2y + 8 = 0, -6 - 2y = -x ,
(4) -2y -5x = 2, -5x = 2y - 4, ( 5 ) 2y + x = 0, 2y = -x + 4, ( 6 ) -2x - y = 1 , -6x = 3y + 3