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Math Help - Simultaneous equation

  1. #1
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    Simultaneous equation

    Been trying to jig this around for a while but i can't seem to get it. I know the basic method for simultaneous equation but this one with x and y as the denominator has thrown me off. Any help would be appreciated.

    2x+3y= 10
    2/x + 3/y = 5
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  2. #2
    Super Member Matt Westwood's Avatar
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    For the 2nd one, multiply top & bottom by xy to simplify it. Then what I'd do would be to substitute for either x or y from the first one, shake it down and then solve the resulting quadratic.
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  3. #3
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    make x the subject in the seccond formula.
    therefore ending up with:x=(4y)/(5y-3)
    substitute for x in the first equation
    after cancelling everything you end up with the quadratic 3y^2-11y+6=0
    factorize it (3y-2)(y-3) =0
    y= 3 and (2/3)
    substitute in tiher equation to get corresponding x values
    (x,y) = (0.5,3) , (4, 2/3)

    but i am a little unsure about the fact that the highest power of both x and y in the two equations is 1 so by right to my knowledge they each should have just one solution, we usually eliminate the negative solution but since both solutions are positives in this one, i am unsure. But never the less the above answers work. (are correct)
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