Inconsistent equations, Dependent equations, independent equations.
Explanation:
If the two equations are independent then the lines intersect at a particular point, and the point (x,y) is the only solution to these equations.
Suppose 2 equations look like to be different, but it defines the same line which shows that these equations has infinite number of solutions.
Sometimes, 2 lines have the same slope, which shows that they are parallel to each other, will never intersect and it has no solution.