AlgebraVery hardNumber of solutions of a system
Algebra practice question
How many solutions does the system 2x − 4y = 8 and x − 2y = 4 have?
- A. Infinitely manyCorrect
- B. Exactly one
- C. None
- D. Exactly two
Answer: A. Infinitely many
Halving the first equation gives x − 2y = 4, the same as the second. The lines coincide.
Why the other answers are wrong
- B. Exactly one
- One solution needs different slopes; these are the same line.
- C. None
- No solution would need parallel but distinct lines; these are identical.
- D. Exactly two
- Two lines can't meet exactly twice.
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