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Math Help - Basic system of linear equations

  1. #1
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    Basic system of linear equations

    I need to determine a value of K for which the system has infinity many solutions

    3x+4y=12
    x+ky=4

    Then

    x=4-(4/3)y

    4-(4/3)y+ky=4
    -(4/3)y+ky=0

    So if k=4/3, then y=y?
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  2. #2
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    Quote Originally Posted by cognoscente View Post
    I need to determine a value of K for which the system has infinity many solutions

    3x+4y=12
    x+ky=4

    Then

    x=4-(4/3)y

    4-(4/3)y+ky=4
    -(4/3)y+ky=0

    So if k=4/3, then y=y?
    If you multiply both sides of the second equation by 3, you'll see

    3x + 4y = 12
    3x + 3ky = 12.

    For the system to have infinitely many solutions, the equations would have to be identically equal.

    That means 3k = 4 and so k = \frac{4}{3}.
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