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Math Help - Simultaneous Equations sorted not

  1. #1
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    Simultaneous Equations sorted not

    Just when I thought I was getting somewhere I still just can't quite crack it

    I have;

    3x + 2y = 3
    5x - 1y = - 8

    I am asked to solve the equations so this is what I have tried

    (3+5)x + (2-1)y = 3 - 8
    8x / 8 = - 5 / 8 = x - 0.625

    3(-0.625) + 2y = 3
    - 1.875 + 2y = 3
    2y = 3 = 1.875
    2y = 4.88
    2y = 4.88
    2 2

    y = 2.44

    Check;

    3(-0.625) + 2(2.44) = 3.00

    5(-0.625) - 1(2.44) = - 5.57

    The latter should be -8?

    Anybody see what I am getting wrong?

    Thanks

    David
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  2. #2
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    Re: Simultaneous Equations sorted not

    Quote Originally Posted by David Green View Post
    Just when I thought I was getting somewhere I still just can't quite crack it

    I have;

    3x + 2y = 3
    5x - 1y = - 8
    Multiply the second equation by 2.
    Add it to the first.
    Solve for x.
    Then solve for y.
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  3. #3
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    Re: Simultaneous Equations sorted not

    Quote Originally Posted by Plato View Post
    Multiply the second equation by 2.
    Add it to the first.
    Solve for x.
    Then solve for y.
    That method does'nt seem to work?

    3x + 2y = 3
    5x - 1y = - 8

    multiplying the second equation by 2

    10x - 2y = - 16
    3x + 2y = 3
    13x - 0 = - 5.33

    x = 0.41

    somewhere I am getting it wrong but can't see it?
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  4. #4
    MHF Contributor Siron's Avatar
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    Re: Simultaneous Equations sorted not

    -16+3=-13 not -5,33 so x=...
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  5. #5
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    Re: Simultaneous Equations sorted not

    Quote Originally Posted by Siron View Post
    -16+3=-13 not -5,33 so x=...
    OK here goes?

    3x + 2y = 3
    5x - 1y = - 8

    10x + 2y = - 16

    3x + 2(10x - 2y) = - 16
    3x + 20x - 4y = - 16

    the rest of this method I don't think works?

    10x - 2y = - 16
    3x + 2y = - 16
    2y = - 16 + 3
    2y = - 13
    y = - 6.5

    3x + 2 (- 6.5) = 3
    3x - 13 = 3
    3x = 16

    x = 5.33

    3(5.33) + 2(-6.5) = 15.99 - 13 = 2.99 almost there?

    5(5.33) - 1(-6.5) = 26.65 - 6.5 = 20.15?????? definately not - 8????
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  6. #6
    MHF Contributor Siron's Avatar
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    Re: Simultaneous Equations sorted not

    What you did in your previous post was fine, by following Plato's hint and multiplying the second equation with 2 and make the addition between the two equations gives:
    13x-0=-13 \Leftrightarrow 13x=-13 \Leftrightarrow x=-1
    Now determine y
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  7. #7
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    Re: Simultaneous Equations sorted not

    why are you making this so difficult?

    3x + 2y = 3
    5x - 1y = - 8

    multiply 2nd equation by 2 and add the equations term for term ...

    3x + 2y = 3
    10x - 2y = -16
    -----------------
    13x = -13

    x = -1
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  8. #8
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    Re: Simultaneous Equations sorted not

    Quote Originally Posted by skeeter View Post
    why are you making this so difficult?

    3x + 2y = 3
    5x - 1y = - 8

    multiply 2nd equation by 2 and add the equations term for term ...

    3x + 2y = 3
    10x - 2y = -16
    -----------------
    13x = -13

    x = -1
    It is difficult not to make something hard when one does not know what one is doing?

    I'll try again with all the help so far, which I must say thank you to all.

    3x + 2y = 3
    5x - 1y = - 8

    10x - 2y = - 16
    3x +2y = 3
    13x = - 13

    x = - 1

    3x + 2y = 3

    3(-1) + 2y = 3
    -3 + 2y = 3

    2y = 3 + 3
    y = 3

    3x + 2y = 3

    3(-1) + 2(3) = -3 + 6 = 3

    5x - 1y = - 8

    5(-1) - 1(3) = - 5 - 3 = - 8

    so x = -1 and y = 3

    Thanks all, I am still learning.
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  9. #9
    MHF Contributor Siron's Avatar
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    Re: Simultaneous Equations sorted not

    Correct!
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