Question

Which equation, when graphed with the given equation, will form a system that has no solution?

Answer 1

The correct answer is B.

This is because for two lines to have no solutions they must have the same slope and different y intercepts. In this case we can distribute the -3 in the B equation and see this is precisely what we get.

y = -3(x + 6)

y = -3x - 18

Since the slopes are now the same in both equations (-3) and the intercepts are different (6 and - 18), we know they are parallel and have no solution.