Unique solution condition for linear system

CAT 2020 Slot 3 · QA · Easy · Linear Equations

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Let kk be a constant. The equations kx+y=3kx + y = 3 and 4x+ky=44x + ky = 4 have a unique solution if and only if

  1. A.

    |k| = 2

  2. B.

    k \neq 2

  3. C.

    |k| \neq 2

  4. D.

    k = 2

Answer

C

Explanation

For a system of linear equations a1x+b1y=c1a_1x + b_1y = c_1 and a2x+b2y=c2a_2x + b_2y = c_2 to have a unique solution: a1a2≠b1b2\frac{a_1}{a_2} \neq \frac{b_1}{b_2}.

Here, k4≠1k  ⟹  k2≠4  ⟹  ∣k∣≠2\frac{k}{4} \neq \frac{1}{k} \implies k^2 \neq 4 \implies |k| \neq 2.

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