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Math Help - Help with nonlinear systems!

  1. #1
    Newbie
    Joined
    Apr 2008
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    2

    Help with nonlinear systems!

    x^2+y^2=25
    y-x=1

    and

    x^2+y^2=5
    xy=2

    please help
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  2. #2
    Senior Member
    Joined
    Dec 2007
    From
    Anchorage, AK
    Posts
    276
    In both cases, solve the second equation for one variable in terms of the other, and then substitute into the first. For example, with:
    x^2+y^2=25
    y-x=1
    we can solve the second for y:
    y=1+x
    and substituting into the first equation:
    x^2+(1+x)^2=25
    2x^2+2x+1=25
    2x^2+2x-24=0
    x^2+x-12=0
    (x-3)(x+4)=0
    so x=3 or x=-4, and substituting into the second equation, we get y=4 or y=-3 respectively, so we have (3,4) and (-4,-3) as solutions.

    The second can be solved similarly.

    --Kevin C.
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  3. #3
    Newbie
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    Apr 2008
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    thanks twisted
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