What does coinciding lines indicate when graphing a system?

What does coinciding lines indicate when graphing a system?

• A. Infinite solutions
• B. No solution
• C. A unique solution
• D. No relation

Answer: (A)

When two lines coincide, they are the same line drawn twice. Every point on that line satisfies both equations, so there are infinitely many points that solve the system. In other words, the solution set is the entire line. By contrast, intersecting lines give a single point (a unique solution), and parallel but distinct lines give no solution.

When two lines coincide, they are the same line drawn twice. Every point on that line satisfies both equations, so there are infinitely many points that solve the system. In other words, the solution set is the entire line. By contrast, intersecting lines give a single point (a unique solution), and parallel but distinct lines give no solution.