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Rajan@2021
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Find the value of k for which the following systems of equations has a unique solution: 4x-5y=k, 2x-3y=12

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This is the basic and conceptual question from linear equations in two variables in which we have given two equations 4x-5y=k, 2x-3y=12 and we have to find the value of k and also asked to solve the equations in such a way that it has a unique solution

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 3D, question no 8

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1 Answer

  1. Given system of equations is
    4x5y=k...(1)
    2x3y=12...(2)

    Here
    a1=4, b1=5, c1=k
    a2=2, b2=3, c2=12

    Condition for the system to have unique solution is
    a1/a2≠b1/b2
    Here, a1/a2=4/2=2   and   b1/b2=5/3
    Clearly 2≠5/7

    Therefore, the given system will always have unique solution.
    Therefore, k is any real number.

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