Mathematics Linear Equations in Two Unknowns

Let the 2 equations be :
Ax + By = C and
ax + by = c.
If A/B = a/b, then the 2 equations have 0 number of solutions because they are parallel to each other.
If A/B is not equal to a/b, then the 2 equations have 1 solution because they are not parallel to each other.
If Ax + By - C = a x+by - c, then the 2 equations have infinite number of solutions because they are identity, not equation.