AlgebraHardConstant that makes a system have no solution
Algebra practice question
The system 3x − ky = 7 and 6x − 8y = 5 has no solution, where k is a constant. What is the value of k?
Answer: 4
No solution means parallel lines: the coefficients must be proportional. 3/6 = k/8 gives k = 4. (The constants 7 and 5 are not in the same ratio, so the lines are distinct, not identical.)
Common wrong answers
- If you answered 2
- 2 comes from 6/3, the ratio of the x-coefficients, not the value of k.
- If you answered 16
- 16 comes from 3k = 6 × 8 with the ratio set up wrongly; 3/6 = k/8 gives 2k = 8.
- If you answered -4
- −4 gets the sign wrong; both y-coefficients are already negative.
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