If the system consists of two identical equations, what is the number of solutions?

If the system consists of two identical equations, what is the number of solutions?

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

Answer: (B)

Two identical equations describe the same line. Every point on that line satisfies both equations, so there are infinitely many possible solutions for the pair of variables. In a two-variable system, a single linear equation already has infinitely many solutions along its line, and repeating it doesn’t narrow that set. This distinguishes it from parallel lines (no solution) or two distinct lines that cross (one solution).

Two identical equations describe the same line. Every point on that line satisfies both equations, so there are infinitely many possible solutions for the pair of variables. In a two-variable system, a single linear equation already has infinitely many solutions along its line, and repeating it doesn’t narrow that set. This distinguishes it from parallel lines (no solution) or two distinct lines that cross (one solution).