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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: (k-1)x-y=5, (k+1)x+(1-k)y=(3k+1)

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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 (k-1)x-y=5, (k+1)x+(1-k)y=(3k+1) and we have to find the value of k for which the following equations has infinite solutions

Kindly solve the above equations

RS Aggarwal, Class 10, chapter 3D, question no 19

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1 Answer

  1. The given system of equations:

    (k – 1)x – y = 5

    ⇒ (k – 1)x – y – 5 = 0 ….(i)  And,

    (k + 1)x + (1 – k)y = (3k + 1)

    ⇒ (k + 1)x + (1 – k)y – (3k + 1) = 0 …(ii)

    These equations are of the following form:  a1x+b1y+c1 = 0, a2x+b2y+c2 = 0  where, a1 = (k – 1), b1= -1, c1 = -5 and a2 = (k + 1), b2 = (1 – k), c2 = -(3k + 1)

    For an infinite number of solutions, we must have:

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