If 2 equations have the same slope but different y-intercepts, how do we classify this system of equations?

Question

Inconsistent

Consistent Independent

Consistent Dependent

Answer 1

It is kind of a matrix algebra, linear algebra problem.

For parallel not coincident lines, solving the matrix problem

finding line intersection

with guassian elimination ends with 0=k where k is a constant not zero

so there is no intersection point and the answer

would be inconsistent since 0=k is a contradiction.

Answer 2

How many commont points (solutions) do the two equation have?