Question

How Many Solutions Does A System Of Two Linear Equations Have If the slope of each equation is different and the y intercepts are the same ?

Answer 1

One solution. 

The solution is that exact point, where the y-intercept(s) is(are). 

Answer 2

Their slopes are different that means these two lines are not parallel and meet at a point.
Since they have y-intercept,they meet at some point ;say (0,c).

So only one solution at y-intercept