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Rajan@2021
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Find the value of k for which the system of linear equations has an infinite number of solutions: kx+3y=(2k+1), 2(k+1)x+9y=(7k+1)

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This is the basic and conceptual question from linear equations in two variables in which we have given two equations kx+3y=(2k+1), 2(k+1)x+9y=(7k+1) and we have to find the value of k for which it has infinite solutions

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 3D, question no 17

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1 Answer

  1. For the system of equations to have infinitely many solutions, the lines must coincide.

    The ratio of corresponding coefficients must be equal.

    ⇒k/2(k+1)=3​/9=(2k+1)/(7k+1)

    Equation 1st and 2nd equality ;

    9k=6(k+1)

    k=2

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