AlgebraVery hardNumber of solutions of a system with proportional coefficients
Algebra practice question
How many solutions does the system 3x + 6y = 9 and x + 2y = 4 have?
- A. NoneCorrect
- B. Exactly one
- C. Infinitely many
- D. Exactly two
Answer: A. None
Dividing the first equation by 3 gives x + 2y = 3, but the second says x + 2y = 4. Same slope, different lines: parallel, no solution.
Why the other answers are wrong
- B. Exactly one
- One solution needs different slopes.
- C. Infinitely many
- Infinitely many would need the second equation to be x + 2y = 3.
- D. Exactly two
- Two lines meet at most once.
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