CAT 2020 Quant Question [Slot 3] with Solution 04

Question

Let k be a constant. The equations kx + y = 3 and 4x + ky = 4 have a unique solution if and only if

  1. |k| ≠ 2
  2. |k| = 2
  3. k ≠ 2
  4. k = 2
Option: 1
Solution:

Simultaneous equation have a unique solution only if \(\frac{{{a_1}}}{{{a_2}}} \ne \frac{{{b_1}}}{{{b_2}}}\)

From the given equations, a unique solution would exist only if \(\frac{k}{2} \ne \frac{2}{k}\)

\( \Rightarrow {k^2} \ne 4 \Rightarrow |k| \ne 2\)

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