AlgebraVery hardRecognizing a dependent system
Algebra practice question
How many solutions (x, y) does the system 3x − y = 4 and 6x − 2y = 8 have?
- A. Infinitely manyCorrect
- B. Exactly one
- C. None
- D. Exactly two
Answer: A. Infinitely many
The second equation is the first multiplied by 2, so both describe the same line; every point on it is a solution.
Why the other answers are wrong
- B. Exactly one
- One solution requires two different intersecting lines, but these are the same line.
- C. None
- No solution requires parallel distinct lines; here the constants scale with the coefficients.
- D. Exactly two
- Two distinct lines can share at most one point; no linear system has exactly two solutions.
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