AlgebraHardNumber of solutions of a system
Algebra practice question
How many solutions does the system 3x + y = 7 and 6x + 2y = 10 have?
- A. NoneCorrect
- B. Exactly one
- C. Exactly two
- D. Infinitely many
Answer: A. None
Doubling the first equation gives 6x + 2y = 14, but the second says 6x + 2y = 10. Same slope, different lines: parallel, no solution.
Why the other answers are wrong
- B. Exactly one
- One solution needs different slopes; these are the same.
- C. Exactly two
- Two lines meet at most once.
- D. Infinitely many
- Infinitely many would need the second equation to be exactly double the first (6x + 2y = 14).
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