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Math Help - simultaneous equation

  1. #1
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    simultaneous equation

    hi, im not really sure what to do on this simultaneous equation, here is the question:
    simultaneous equation-question.jpg

    i can do simultaneous equations but this one has got me, so any help will be much appreciated!!

    thanks!
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  2. #2
    MHF Contributor harish21's Avatar
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    \boxed{y=3x-11}\;\hdots (1)

    \boxed{x^2+2xy+3=0}\;\hdots (2)

    substitute (1) in (2)

    x^2+2x(3x-11)+3=0

     x^2+6x^2-22x+3=0

    7x^2-22x+3=0

    solve for x and then find y
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  3. #3
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    im not sure how to find x this way, i don't think i have done it like this before.
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  4. #4
    MHF Contributor harish21's Avatar
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    Are you serious?

    You have just done quadratic equations in one of your other post.. Follow the same procedure..

    \boxed{7x^2-22x+3=0} is a quadratic equation!! Follow the same procedure as you did in THIS POST OF YOURS
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  5. #5
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    yes i know how to do the quadratic equation but how would have get x and y??
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  6. #6
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    e^(i*pi)'s Avatar
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    Substitution is the only way to solve this because you have different powers of x

    You can solve that quadratic to give two values of x:

    7x^2-22x+3 = (7x-1)(x-3) = 0

    Using those two values of x plug into equation 1 to find their corresponding y values (you will get two pairs of solutions as a final answer)


    edit: an example

    you know that x = 3 is one of the roots and so you can sub x=3 into eq1 to find y: y = 3(3) - 11 = -2

    Hence (3, -2) is one pair of solutions. Can you do the same thing for the other root?
    Last edited by e^(i*pi); January 17th 2011 at 07:48 AM. Reason: see post
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  7. #7
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    for the quadratic equation answers i get:
    simultaneous equation-answers.jpg

    which is X and which is Y?
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  8. #8
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    so x=3 and y=-6 ??
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  9. #9
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    Quote Originally Posted by andyboy179 View Post
    so x=3 and y=-6 ??
    NO! Please quit guessing.

    There are 2 solutions for x: your previous post shows you got them: x = 3 or x = 1/7.

    Now substitute EACH in the equation y = 3x - 11; you will get 2 corresponding solutions for y ; kapish?

    Are you attending math classes?
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  10. #10
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    on both of them i got -2 and -10.58??

    no, only at school
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  11. #11
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    e^(i*pi)'s Avatar
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    -2 is fine (as worked out in post 6) but \dfrac{3}{7} - 11 = -\dfrac{74}{7} \approx 10.57 (the next digit is a 1)

    You need to express the roots as pairs though to assign the y values you just found to the x values you used to get them
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  12. #12
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    i don't understand "(the next digit is a 1)"
    so x=3
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  13. #13
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    would this work?
    for X i get 3 and 0.14
    for Y i get -2 and -10.58

    would X=3 and Y=-2 in the end???
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  14. #14
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    The next digit is a 1 means I rounded down 10.571 to 10.57

    For example you found that when x = 3, y = -2 so a pair is (3,-2)

    yes x=3 and y=-2 does work and x = 0.14 and y = -10.57 work
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  15. #15
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    so for my answer i could put either one of x=3 and y=-2 and x = 0.14 and y = -10.57.
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