A) One solution: there is independence between the equations for the lines, so the lines can have the same y intercept but must have different slopes. These lines will always intersect somewhere.
B) No solution: the lines are parallel, so they have the same slope and different y intercepts.
C) an infinite number of solutions: there is dependence between the equations. If both equations are written in standard form, one will be a multiple of the other, so effectively they are a single equation.
Graphically, A appears as crossed lines; B appears as two parallel lines; C is one single line.
Note that an equation involving only one variable, e.g., y=a or x=b, where a and b are numbers, may be regarded as examples of A or B.
y=a and x=b intersect at (b,a); y=a and y=b, or x=a and x=b, are parallel.