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Math Help - Help solving difficult simultaneous quadratic equation

  1. #1
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    Help solving difficult simultaneous quadratic equation

    I'm stuck on a problem in an exercise book. It gives the answer, but I just can't get the same answer. Here's the problem:


    Find the co-ordinates of the point of intersection of the given straight line and curve:

    i. 2x - 5y =6
    ii. 2xy - 4x - 3y = 1


    Following an example earlier in the book, I went this way:


    i. 2x = 6 + 5y
    i. 4x = (6 + 5y) = (6 + 5y)(6 + 5y) = 36 + 60y + 25y


    i into ii:


    ii. y(6 + 5y) -(36 + 60y + 25y) - 3y = 1
    ii. 6y + 5y -36 - 60y - 25y -3y = 1
    ii. -20y - 57y - 37 = 0


    When I put that last line into the quadratic formula, I only get one root. The given answer has two. I'm clearly doing something wrong. Would someone please help?
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  2. #2
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    Re: Help solving difficult simultaneous quadratic equation

    Quote Originally Posted by markling View Post
    I'm stuck on a problem in an exercise book. It gives the answer, but I just can't get the same answer. Here's the problem:


    Find the co-ordinates of the point of intersection of the given straight line and curve:

    i. 2x - 5y =6
    ii. 2xy - 4x - 3y = 1


    Following an example earlier in the book, I went this way:


    i. 2x = 6 + 5y
    i. 4x = (6 + 5y) = (6 + 5y)(6 + 5y) = 36 + 60y + 25y


    i into ii:


    ii. y(6 + 5y) -(36 + 60y + 25y) - 3y = 1
    ii. 6y + 5y -36 - 60y - 25y -3y = 1
    ii. -20y - 57y - 37 = 0


    When I put that last line into the quadratic formula, I only get one root. <--- I get: y=-1 or y = -\frac{37}{20} !
    The given answer has two. I'm clearly doing something wrong. Would someone please help?
    ... and consequently x = \frac12~\vee~x=-\frac{13}8
    Last edited by earboth; June 4th 2012 at 08:00 AM.
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  3. #3
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    Re: Help solving difficult simultaneous quadratic equation

    Agh. Such a silly mistake. Thanks very much, earboth. I can now see what I was doing wrong. I've been leaving my equations in whatever order they come out, and then they've been getting garbled when I put them into the quadratic formula. So on paper I didn't have -20y - 57y - 37 = 0, I had -57y -20y - 37 = 0. And then I was putting a in as b and b in as a. Thanks again.
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