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Math Help - system of equations

  1. #1
    Member
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    Nov 2010
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    system of equations

    Hello, I am wondering if I have gone about this system of equations correctly ?

    3x+5 = AX+2A+BX+B

    using x = 0
    5 = 2A+B

    using x = 1
    8 = 3A + 2B

    therefore:
    5 = 2A+B
    8 = 3A + 2B

    cancelling a term:
    10 = 4A+2B
    8 = 3A + 2B

    equals:
    A = 2
    B= 1
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  2. #2
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    Lexington, MA (USA)
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    Re: system of equations

    Hello, fran1942!

    Hello, I am wondering if I have gone about this system of equations correctly ?

    3x+5 = AX+2A+BX+B

    using x = 0
    5 = 2A+B

    using x = 1
    8 = 3A + 2B

    therefore:
    5 = 2A+B
    8 = 3A + 2B

    cancelling a term:
    10 = 4A+2B
    8 = 3A + 2B

    equals:
    A = 2
    B= 1

    You're absolutely correct! . . . Good work!


    Here's another approach . . .

    We have: . 3x + 5 \:=\:(A+B)x + (2A+B)

    Two polynomials are equal if their corresponding coefficients are equal.

    Hence: . \begin{Bmatrix}A + B &=& 3 \\ 2A + B &=& 5 \end{Bmatrix}

    which yields the same answers: . \begin{Bmatrix} A &=& 2 \\ B &=& 1 \end{Bmatrix}

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