If a system of linear equations has lines with different slopes and the same y-intercept, the system will have one unique solution. This is because the lines will intersect at exactly one point, which is the point where both equations are satisfied.
The fact that the lines have different slopes ensures that they are not parallel, so they will not be consistent and independent, leading to a single point of intersection. The common y-intercept means that this point of intersection will lie on the y-axis at the shared y-value. The coordinates of the solution will be given by this y-intercept and the corresponding x-value where the two lines meet.
