If the y-intercepts are the same, then the two linear have the same y-intercept as a solution. That is one common solution for both expressions. The two expressions intersect at that point. Since the slopes are different, there are no more common solutions since if two different lines intersect, they intersect at exactly one point and no more.
Answer: 1 intersection
Check the picture below.
in the picture below, the bottom part
notice, 69° + 21° = 90°, so 21° and 69° are really complementary angles, sharing the same quadrant, meaning for any two sides of lengths say, a,b one angle will have a tangent of say b/a, then the other will have a tangent of a/b.
namely the tangent of each angle, is simply the other's tangent upside-down.