If two lines are parallel and not the same line, how many solutions does the system have?

If two lines are parallel and not the same line, 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 are parallel and not the same line, they never meet. A solution to the system would be a point that lies on both lines at once, but there isn’t any such point because the lines never cross. So there are zero solutions. If the lines were the same line, there would be infinitely many solutions since every point on the line satisfies both equations. If they intersect, there would be exactly one solution at the intersection point. Here, the distinct parallel relationship means no shared point.

When two lines are parallel and not the same line, they never meet. A solution to the system would be a point that lies on both lines at once, but there isn’t any such point because the lines never cross. So there are zero solutions. If the lines were the same line, there would be infinitely many solutions since every point on the line satisfies both equations. If they intersect, there would be exactly one solution at the intersection point. Here, the distinct parallel relationship means no shared point.