If two equations represent the same line, how many solutions are there?

If two equations represent the same line, how many solutions are there?

• A. No Solution
• B. One Solution
• C. Infinitely many solutions
• D. The lines intersect at a single point

Answer: (C)

When two equations describe the same line, every point on that line satisfies both equations. That means there are infinitely many points in common, so the solution set has infinitely many solutions. If the lines were parallel but different, there would be no point common to both, giving no solution. If they intersect at exactly one point, there would be one solution. But describing the same line means the entire line is the solution.

When two equations describe the same line, every point on that line satisfies both equations. That means there are infinitely many points in common, so the solution set has infinitely many solutions.

If the lines were parallel but different, there would be no point common to both, giving no solution. If they intersect at exactly one point, there would be one solution. But describing the same line means the entire line is the solution.