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Math Help - simultaneous equation

  1. #1
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    simultaneous equation

    hi, could someone please show me the steps involved in solving the simultaneous equation:
    y = x - 8
    x^2 + y = 4

    and could you tell me why you choose that particular path to get the answer

    thankyou, Mark
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  2. #2
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    Quote Originally Posted by mark View Post
    hi, could someone please show me the steps involved in solving the simultaneous equation:
    y = x - 8
    x^2 + y = 4

    and could you tell me why you choose that particular path to get the answer

    thankyou, Mark
    Sub eq1 into eq2 and rearrange to get

    x^2+x-12=0 \: \rightarrow (x-3)(x+4)=0

    Sub those two solutions back into eq1 to give you two pairs of solutions

    Spoiler:
    (3,-5) and (-4,-12)
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  3. #3
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    (1)
    (2)

    re arrange (2)

    y = 4 - x^2

    putting this back into (1)

    4 - x^2 = x - 8
    x^2 + x - 12 = 0
    (x+4)(x-3) = 0
    x = -4 or 3

    when x = -4 (1) y = -4 -8 = -12 (2) (-4)^2 + y = 4 16 + y = 4 = -12

    when x = 3 (1) y = 3 - 8 = -5 (2) (3)^2 + y = 4 9 + y + 4 = -5

    therefore 2 answers fulfil this sim equation

    x = -4 y = -12
    x = 3 y = -5

    I did it this way as when I saw a x squared I automatically knew it could have a negative value as well as a positive.
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