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Rajan@2021
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For what value of the value of k does the following pair of linear equations have indefinitely many solutions: 10x+5y-(k-5)=0, 2x+10y-k=0

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An important and exam oriented question from linear equations in two variables in which we have given two equations 10x+5y-(k-5)=0, 2x+10y-k=0 and we have been asked to find the value of k for which the given equations have indefinitely many solutions

Kindly give me a detailed solution of this question

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

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1 Answer

  1. 10x+5y−(k−5)=0and
    20x+10y−k=0
    These given equations are in the form:
    a1​x+b1​y+c1​=0 and
    a2​x+b2​y+c2​=0
    Where
    a1​=10,b1​=5 and c1​=−(k−5)
    a2​=20,b2​=10 and c2​=−k
    System has infinitely many solutions.
    10/20​=5/10​=−(k−5)/-k​=(k−5)/k​
    5k=10k−50
    or k=10
    The value of k is 10.

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