Two lines have the same slope but different y-intercepts. How many solutions does the system have?

Two lines have the same slope but different y-intercepts. How many solutions does the system have?

• A. No solution
• B. One solution
• C. Infinitely many solutions
• D. The lines are the same line

Answer: (A)

When two lines share the same slope, they are parallel. If their y-intercepts are different, they are two distinct parallel lines that do not cross each other. A solution to the system would be a point where both lines meet, but there isn’t one here. So there are no solutions. For contrast: if the lines crossed once, there would be one solution; if they were the same line, there would be infinitely many solutions.

When two lines share the same slope, they are parallel. If their y-intercepts are different, they are two distinct parallel lines that do not cross each other. A solution to the system would be a point where both lines meet, but there isn’t one here. So there are no solutions. For contrast: if the lines crossed once, there would be one solution; if they were the same line, there would be infinitely many solutions.