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System of Linear Equations with No Solution

CAT 1991 Slot 1 · Quantitative Ability · Easy · Algebra

This is an easy Quantitative Ability question from the CAT 1991 Slot 1 paper. It tests Algebra. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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What is the value of kk for which the following system of equations has no solution? 2x−8y=32x - 8y = 3 kx+4y=10kx + 4y = 10

  1. A.

    -2

  2. B.

    1

  3. C.

    -1

  4. D.

    2

Answer

C

Explanation

For no solution, the lines must be parallel and distinct: a1a2=b1b2≠c1c2  ⟹  2k=−84≠310\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2} \implies \frac{2}{k} = \frac{-8}{4} \neq \frac{3}{10} 2k=−2  ⟹  k=−1\frac{2}{k} = -2 \implies k = -1

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