Matt and Brian were solving a system of equations. They both noticed that the two lines had the same slope. Brian said that because each line in the system had the same slope, the two lines had to be parallel, which meant the solution to the system was "no solutions." Matt disagreed, and said they should also look at the y-intercepts before determining how many solutions there were. Who is correct? A. Brian is correct. When two lines have the same slope, they are always parallel. B. Matt is correct. Though two lines with equal slopes are often parallel, if they have the same y-intercept, they are the same line and have infinitely many solutions. C. Neither person makes a valid argument.

Accepted Solution

Brian understands this situation better than does Matt.Β Β 

If two lines have the same slope, these lines could be either coincidential (one lying on top of the other) or parallel and never intersecting.