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Math Help - find the values of the coefficients

  1. #1
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    find the values of the coefficients

    For what values of the coefficients a and b is (2,-1) the solution to the following linear system?

    ax + by = -7
    2ax -3by = 1

    (Answer: a= -2, b= 3)

    I've been taught to find the values of x and y by substitution or elimination, but how do you find the values of the coefficients a and b is (2,-1) as in the above question?

    Please help.
    Thanks.
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  2. #2
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    Quote Originally Posted by shenton View Post
    For what values of the coefficients a and b is (2,-1) the solution to the following linear system?
    ax + by = -7
    2ax -3by = 1

    (Answer: a= -2, b= 3)

    I've been taught to find the values of x and y by substitution or elimination, but how do you find the values of the coefficients a and b is (2,-1) as in the above question?
    Please help.
    Thanks.
    Hi,

    you know the values of x and y: x = 2 and y = -1.

    Plug in these values into your equations:

    2a - b = -7
    4a + 3b = 1

    Now you have a linear system in (a,b) which you can solve as usual.

    EB
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  3. #3
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    I never realize I could just plug in those values like that.

    This is really an eye opener for me.

    Thanks, earboth for showing me how.
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