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Find the value of k for which the system of linear equations has an infinite number of solutions: 2x+(k-2)y=k, 6x+(2k-1)y=(2k+5)

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This is the basic and exam oriented question from linear equations in two variables in which we have given two equations 2x+(k-2)y=k, 6x+(2k-1)y=(2k+5) and we have been asked 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 16


1 Answer

  1. For the system to have infinitely many solutions, lines must coincide each other

    ratio of respective coefficients must be equal (x, y and constant coefficients)


    Equate first two equations ;



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