Question

Naomi solves a system of equations using substitution. The system has infinitely many solutions. Which of the following could be the last step in Naomi's solution?
A. x = 0
B. 3 = –3
C. 2 = 2
D. 5 = y

Answer 1

In a system of equations that has infinitely many solutions, the last step usually indicates that the equations are dependent, meaning they represent the same line or plane in a geometric sense.

Among the options provided:
- **A. x = 0** - This indicates a specific value for x, suggesting a unique solution rather than infinitely many.
- **B. 3 = –3** - This is a contradiction and does not imply any solutions, let alone infinitely many.
- **C. 2 = 2** - This is a tautology, indicating that the equations are dependent and therefore can have infinitely many solutions. This is a potential candidate.
- **D. 5 = y** - This represents a specific relationship between y and a constant, implying a specific solution rather than infinitely many.

Based on this analysis, the option that could realistically represent the last step in Naomi's solution, indicating the presence of infinitely many solutions, is:

**C. 2 = 2**