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For what value of k does the system of ...

For what value of k does the system of equations
` " " x + 2y = 3, 5x + ky + 7 = 0`
have (i) a unique solution, (ii) no solution ?
Also, show that there is no value of k for which the given system equations has infinitely many solutions.

Answer

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Knowledge Check

  • For what values of k, does the system of linear equations x + y + z = 2, 2x + y - z = 3, 3x + 2y + kz = 4 have a unique solution ?

    A
    k = 0
    B
    `-1 lt k lt 1`
    C
    `-2 lt k lt 2`
    D
    `k ne 0`

  • The value of K for which the system of equations x+2y+7=0 and 2x+ky+14=0 have infinitely many solutions is

    A
    2
    B
    4
    C
    6
    D
    8

  • For what values of k is the system of equations k x + 3y = k - 2 12 x + ky = k inconsistent ?

    A
    `k =pm 6`
    B
    `k = -6` only
    C
    `k = 6` only
    D
    none of these

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    What is the value of k , for which the simultaneous equations 2x+3y=8 and 6x-ky=24 have infinitely many solutions ?

    Find the value of k for which the system of equations kx-4y =3, 7x -2y =5 has a unique solution.

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