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Rajan@2021
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For what value of k does the system of equations x+2y=5, 3x+ky+15=0 have a (i) unique solution (ii) no solution?

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One of the most important and conceptual question from linear equations in two variables in which we have given two equations x+2y=5, 3x+ky+15=0 and we have to find the value of k for which it has a unique solution and also asked to solve for which it has no solution

Kindly solve the above equations

RS Aggarwal, Class 10, chapter 3D, question no 13

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1 Answer

  1. (i)

    x+2y=5,3x+ky+15=0
    Here,

    a1=1, b1=2, c1=5
    a2=3, b2=k, c2=15

    a1/a2=1/2, b1/b2=2/k, c1/c2=−5​/15=−1/3
    a unique solution

    a1/a2≠b1/b2⇒1/2≠2/k

    k≠4
    (ii) a1/a2≠b1/b2≠c1/c2
         1/2=2/k≠-1/3
         k=4

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