![]() If Aubrey finds that the slopes of the lines are the same and the y-intercepts are different, then she can be confident that her answer is correct. Solution Solve the first equation for y x + 3y - x 3 - x 3y -x + 3. In the case of this system, neither line goes through the origin, but the lines are still parallel. The origin has no bearing on whether two lines are parallel. If Aubrey finds that the slopes of the lines are the same and the y-intercepts are different, then she can be confident that her answer is correct. Parallel lines have the same slope, but she also has to check whether they have different y-intercepts because the lines could be collinear (remember that 2 collinear lines are the same line).
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