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Rajan@2021
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Find k for which the system kx-y=2, 6x-2y=3 has a unique solution.

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One of the most important and exam oriented question from linear equations in two variables in which we have given two equations kx-y=2, 6x-2y=3 and we have to find the value of k for which the given equations have a unique solution.

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, Chapter 3F, question no 17

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1 Answer

  1. The given system of equations is
    kx−y−2=0
    6x−2y−3=0

    It is of the form a1​x+b1​y+c1​=0
    a2​x+b2​y+c2​=0,

    where a1​=k, b1​=−1, c1​=−2 and a2​=6, b2​=−2 and c2​=−3

    (i) The given system will have a unique solution, if

    a1/a2​​≠b1/b2 i.e, if k/6≠−1/-2​ i.e., k≠3

    So, the given of equations system will have a unique solution, if k≠3.

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