If the two equations describe the exact same line, what is the nature of the solution set?

If the two equations describe the exact same line, what is the nature of the solution set?

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

Answer: (D)

Two linear equations describe the same line means they are just different ways of writing the same relationship between x and y. 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. This happens when the equations are essentially the same line (one is a multiple of the other or they simplify to the same equation). If they were parallel but not identical, there would be no solution; if they intersect at a single point, there would be exactly one solution.

Two linear equations describe the same line means they are just different ways of writing the same relationship between x and y. 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. This happens when the equations are essentially the same line (one is a multiple of the other or they simplify to the same equation). If they were parallel but not identical, there would be no solution; if they intersect at a single point, there would be exactly one solution.