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NDA 2023 Maths · Mathematics · Matrices · medium

The system x+2y=3, 2x+ky=5 has no solution for k equal to

Single correct option

The system x+2y=3x+2y=3, 2x+ky=52x+ky=5 has no solution for kk equal to
  1. A. 22
  2. B. 11
  3. C. 44
  4. D. −4-4
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Answer: (C) 44

The coefficient ratio 12=2k\dfrac12=\dfrac2k gives k=4k=4 (parallel lines). For k=4k=4 the second equation is 2x+4y=52x+4y=5, while twice the first is 2x+4y=62x+4y=6; since 5≠65\ne6 the system is inconsistent. For all other kk the solution is unique, and k=4k=4 with RHS 66 would give infinitely many solutions.
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