AlgebraHardConstant that makes a system inconsistent
Algebra practice question
For what value of k does the system 6x + ky = 12 and 3x + 4y = 5 have no solution?
- A. 8Correct
- B. 2
- C. 4
- D. 24/5
Answer: A. 8
No solution means parallel distinct lines: coefficients proportional (6/3 = k/4, so k = 8) while the constants break the proportion (12/5 ≠ 2).
Why the other answers are wrong
- B. 2
- 2 is the ratio 6/3 itself; k must satisfy k/4 = 2, so k = 8.
- C. 4
- k = 4 gives slopes −6/4 and −3/4, which differ — the lines would cross once.
- D. 24/5
- 24/5 forces the constants into proportion with 6/3 only if the y-coefficients also matched; the parallel condition is k = 8.
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