When dealing with two linear equations that have no solution, it means that they usually have two variables and are part of a system of equations. Such an example would be the following two equations
2x - y = 2
4x - 2y = 8
These two equations would be part of the same system and they have no solution because there is no pair of values that will give a valid solution to both for the variables x and y. In a graph these equations would appear as parallel lines that never intersect. This is why no solution is found, because there is no intersection.
