Question

In a system of two linear equations, what is the relationship between the slope of the lines and the number of solutions to the system?

Answer 1

Parallel lines will have no solutions unless they are the same line. 

Otherwise, if the slopes are different, it will have exactly one solution. 

Answer 2

When the slopes of two lines are equal, the lines are either parallel or they are the same line. So, equal slopes indicate either no solution to the system or infinitely many solutions to the system.