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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: 2x+3y-5=0, kx-6y-8=0

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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 2x+3y-5=0, kx-6y-8=0 and we have to solve the equations in such a way that it has a unique solution and also we have to find the value of k

Kindly solve the above equations

RS Aggarwal, Class 10, chapter 3D, question no 4

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1 Answer

  1. 2x+2y−5=0.....(1)
    kx−6y−8=0....(2)
    a1​=2, b1​=3, c=​−5
    a2​=k, b2​=−6, c2​=−8
    a1/a2​=2/k​, ​b1​​/b2=3/−6​
    Which shows
    a1/a2≠b1/b2​​
    System has a unique solution.
    Now. Find the value of k:
    2/k≠3/−6
    k≠−4

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