For what value of k does the system of equations kx + 2y = 5 and 3x + y = 1 have no solution? A. k = 6 B. k = 3/2 C. k ≠ 6 D. k = 5/2 Answer: A) k = 6 Explanation: For no solution, a₁/a₂ = b₁/b₂ ≠ c₁/c₂. Here a₁=k, a₂=3, b₁=2, b₂=1, c₁=5, c₂=1. So k/3 = 2/1 → k = 6. Check: 5/1 ≠ 2/1, so no solution when k=6.

imo class 12 determinants

For what value of k does the system of equations kx + 2y = 5 and 3x + y = 1 have no solution?

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For what value of k does the system of equations kx + 2y = 5 and 3x + y = 1 have no solution?

A. k = 6
B. k = 3/2
C. k ≠ 6
D. k = 5/2

Answer: A) k = 6

Explanation: For no solution, a₁/a₂ = b₁/b₂ ≠ c₁/c₂. Here a₁=k, a₂=3, b₁=2, b₂=1, c₁=5, c₂=1. So k/3 = 2/1 → k = 6. Check: 5/1 ≠ 2/1, so no solution when k=6.

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