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Math Help - system of equations

  1. #1
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    system of equations

    solve the system of equations where x,y are variables and a,b are constants:

    x + y = a
    (x^2)*y + x*(y^2) = b
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  2. #2
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    Dear jmedsy,

    x+y=a-------A

    (x+y)xy = axy

    axy=b--------B

    By solving A and B you could easily get the answer.
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  3. #3
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    Hello, jmedsy!

    Exactly where is your difficulty?
    Straight substitution will solve it.


    Solve the system of equations where x,y are variables and a,b are constants:

    . . . \begin{array}{cccc}x + y &= &a & [1] \\<br />
x^2y + xy^2 &=& b & [2] \end{array}

    From [1], we have: . y \:=\:a-x\;\;[3]

    Substitute into [2]: . x^2(a-x) + x(a-x)^2 \:=\:b

    Expand: . ax^2 - x^3 + a^2x - 2ax^2 + x^3 \:=\:b \quad\Rightarrow\quad ax^2 - a^2x + b \:=\:0

    Quadratic Formula: . \boxed{x \;=\;\frac{a^2 \pm\sqrt{a^4-4ab}}{2a}}

    Substitute into [3]: . y \;=\;a - \frac{a^2\pm\sqrt{a^4-4ab}}{2a} \quad\Rightarrow\quad\boxed{ y \;=\;\frac{a^2 \mp\sqrt{a^4-4ab}}{2a}}

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  4. #4
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    I get this answer. When I test the solutions in maple, they work in the first equation but not for the second.



    nevermind i'm doing some really bizarre algebra. everything is ok now, thanks for the help
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  5. #5
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    Mistaken post
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