No solution can only be possible when two lines are parallel to one another, thus never intersect and hence have no solution. In order to identify a two parallel lines, the slope of each must be equal to one another. Let's take a look at our equations:
y=2/3x,
y=2/3x+3
Here 2/3 acts as the slope provided it is a "coefficient" of x. This means that the system has no solution provided the similar slopes.
