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?

Question

Kara Daniel

Mathematics

31 July, 15:20

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?

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Emilie Bridges · Answer 1

Matt is correct, if two lines have the same slope and the same y-intercept, there are infinitely many solutions as both equation describe the same line.

Only two lines with the same slope and different y-intercepts have no solution.