what is the value of k so that the pair of linnear equations kx-y=2 and 6x-2y=3 has a unique solution​

Question

what is the value of k so that the pair of linnear equations kx-y=2 and 6x-2y=3 has a unique solution​

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Alexandra 5 months 2021-12-13T02:39:45+00:00 1 Answer 0 views 0

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    2021-12-13T02:41:03+00:00

    Given,

    Pair of linear equations:

    kx y = 2 ...(1) ; 6x 2y = 3 ...(2)

    On comparing each linear equations with the standard form of linear equation in two variable (i.e., ax + by + c = 0 ), we get

     \\ \\

    a1 = k , b1 = 1 , c1 = 2 { for eq.(1) }

    a2 = 6, b2 = 2, c2 = 3 { for eq.(2) }

     \\ \\ \\

    To Find,

    ☛ value of k such that the following pair of linear equations would have a unique solution.

     \\ \\ \\

    Solution,

    We know,

    for unique solution, the coefficients of two linear equations should follow the following condition.

     \\

     \qquad \sf  \huge{\dfrac{ a_{1} }{ a_{2} }   \ne  \dfrac{ b_{1} }{ b_{2}}}  \\ \\

    On solving further,

     \sf \rightarrow \quad  \dfrac{k}{6}   \ne  \dfrac{  \cancel{-} 1}{ \cancel{ -} 2}  \\  \\  \sf \rightarrow \quad  \frac{k}{6}  \ne  \frac{1}{2}  \\  \\ \sf \rightarrow \quad k \ne  \frac{ \cancel{6}^{3} }{ \cancel{2}_{1} }  \\  \\ \sf \rightarrow \quad k \ne 3 \\  \\  \\

    Here, The value of k can be anything except 3.

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