Which statement describes a system with infinitely many solutions?

Which statement describes a system with infinitely many solutions?

• A. 5 = 4
• B. 5 = 5
• C. 5 ≠ 5
• D. x equals y with inconsistent constants

Answer: (B)

Infinitely many solutions come from equations that don’t actually restrict the variables beyond describing the same set of points. A statement like 5 = 5 is always true, so it adds no restriction at all. If that tautology appears in a system alongside another equation, the solution set is governed by that other equation, which in two variables forms a line with infinitely many points. In contrast, a false statement like 5 = 4 or a contradiction like 5 ≠ 5 forces impossible conditions, giving no solutions. An inconsistency between two equations also yields no solution. So the statement that describes a system with infinitely many solutions is 5 = 5.

Infinitely many solutions come from equations that don’t actually restrict the variables beyond describing the same set of points. A statement like 5 = 5 is always true, so it adds no restriction at all. If that tautology appears in a system alongside another equation, the solution set is governed by that other equation, which in two variables forms a line with infinitely many points. In contrast, a false statement like 5 = 4 or a contradiction like 5 ≠ 5 forces impossible conditions, giving no solutions. An inconsistency between two equations also yields no solution. So the statement that describes a system with infinitely many solutions is 5 = 5.