AlgebraVery hardConditions for infinitely many solutions
Algebra practice question
The system y = mx + 4 and y = 2x + b, where m and b are constants, has infinitely many solutions. Which of the following must be true?
- A. m = 2 and b = 4Correct
- B. m = 2 and b ≠ 4
- C. m ≠ 2
- D. m = 4 and b = 2
Answer: A. m = 2 and b = 4
Infinitely many solutions means the two equations describe the same line: same slope and same intercept.
Why the other answers are wrong
- B. m = 2 and b ≠ 4
- Same slope with different intercepts gives no solution.
- C. m ≠ 2
- Different slopes give exactly one solution.
- D. m = 4 and b = 2
- This swaps slope and intercept.
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