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Rajan@2021
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Find the value of k for which the following pair of linear equations have indefinitely many solutions: 2x+3y=7, (k-1)x+(k+2)y=3k

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This question is taken from linear equations in two variables in which we have given two equations 2x+3y=7, (k-1)x+(k+2)y=3k and we have to find the value of k for which these equations have indefinitely many solutions.

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 3F, question no 2

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  1. 2x+3y=7
    (k1)x+(k+2)y=3k

    These given equations are in the form:
    a1x+b1y+c1=0 and
    a2x+b2y+c2=0

    Where
    a1=2, b1=3 and c1=7
    a2=(k1), b2=(k+2) and c2=3k

    a1/a1​2=2/(k1), b1/b2=3/(k+2),c1/c2=7/3k
    Which shows:
    a1/a2=b1/b2=c1/c2

    System has infinitely many solutions.
    Now, Find the value of k
    2/(k1)=3/(k+2)=7/3k
    2/(k1)=3/(k+2)
    3(k1)=2(k+2)
    which implies, k=7
    The value of k is 7.

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