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Rajan@2021
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For what value of k does the system of equations kx+2y=5, 3x-4y=10 have a (i) unique solution (ii) no solution?

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An important and conceptual question from linear equations in two variables in which we have given two equations kx+2y=5, 3x-4y=10 and we have been asked to find the value of k in such a way that it has a unique solution and also asked to solve these equations in such a way that it has no solution

RS Aggarwal, Class 10, chapter 3D, question no 12

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  1. (i) Here,

    a1​=k, b1​=2, c1​=5
    a2​=3, b2​=−4, c2​=10

    a1/a2​​=k/3, b1/b2​​=2/-4​=−1/2​

    c1/c1​​2=5​/10=1/2​

    System has a unique solution.
    a1/a2≠b1/b2​​⇒k/3≠-1/2​

    k≠−3/2
    (ii) If system has a no solution.

    a1/a2=b1/b2​​≠1/2​

    k/3=−1​/2≠1/2​

    k≠3/2

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