If the two lines are parallel and distinct, the solution set is

If the two lines are parallel and distinct, the solution set is

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

Answer: (D)

When solving a system of linear equations, you’re looking for a point that lies on both lines. If two lines are parallel and distinct, they never cross each other, so there isn’t any point that satisfies both equations at once. That means there is no solution to the system. To compare with other scenarios: if the lines crossed at one point, there would be exactly one solution. If they were the same line, every point on that line would satisfy both equations, giving infinitely many solutions. But with parallel and distinct lines, none of those situations occurs, so the correct description is that there is no solution.

When solving a system of linear equations, you’re looking for a point that lies on both lines. If two lines are parallel and distinct, they never cross each other, so there isn’t any point that satisfies both equations at once. That means there is no solution to the system.

To compare with other scenarios: if the lines crossed at one point, there would be exactly one solution. If they were the same line, every point on that line would satisfy both equations, giving infinitely many solutions. But with parallel and distinct lines, none of those situations occurs, so the correct description is that there is no solution.