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Math Help - Changing the subject of the formulae

  1. #1
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    Changing the subject of the formulae

    Please may someone show me the steps to changing the subject for the following questions, the subject needs to be y for each one.

    1) h-y
    h+y = k

    2) y+3 d
    y-2 = e
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  2. #2
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    Re: Changing the subject of the formulae

    Sorry everything has been moved to the left a little.
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  3. #3
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    Re: Changing the subject of the formulae

    Hello, joe345!

    \text{(1) Solve for }y\!:\;\frac{h-y}{h+y} \:=\:k

    Multiply by (h+y)\!:\;h-y \:=\:k(h+y)

    Expand: . . . . . . . . h-y \:=\: kh + ky

    Get all y-terms to one side:

    . . . . . . . . . . . \text{-}ky - y \:=\:kh - h

    Factor: . . . . \text{-}(k+1)y \:=\:h(k-1)

    Divide by \text{-}(k+1)\!:\;\:y \:=\:\frac{h(k-1)}{\text{-}(k+1)}

    Multiply by \tfrac{\text{-}1}{\text{-}1}\!:\qquad\; y \:=\:\frac{h(1-k)}{1+k}

    [The last step is not necessary, but the answer is neater.]




    \text{(2) Solve for }y\!:\;\frac{y+3}{y-2} \:=\:\frac{d}{e}

    Cross-multiply: . e(y+3) \:=\:d)y-2)

    Expand: . . . . . . ey + 3e \:=\:dy - 2d

    Get y-terms on one side:

    . . . . . . . . . ey - dy \:=\:\text{-}3e -2d

    Factor: . . . (e-d)y \:=\:\text{-}(3e+2d)

    Divide by (e-d)\!:\; y \:=\:\frac{\text{-}(3e+2d)}{e-d}

    Multiply by \tfrac{-1}{-1}\!:\quad\; y \:=\:\frac{2d+3e}{d-e}
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  4. #4
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    Re: Changing the subject of the formulae

    Thankyou very much
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