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Math Help - Solution to 3 simultaneous equations

  1. #1
    Senior Member bugatti79's Avatar
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    Solution to 3 simultaneous equations

    Folks,

    I am struggling with this seemingly simple task of solving for s and t in terms of x and y to ultimately get u in terms of x and y.

    x=s+st/4+t^2/4 (1)
    y=s+t (2)
    u=s/4+t/2 (3)

    My attempt is as follows: From eqn 1 find t, its a quadratic in t
    t=\frac{-s+- \sqrt {s^2+4(4x-4s)}}{2} (4)

    From (2) find t t=y-s (5)

    Then equate 4 and 5???.... Im actually lost....

    The answers are

    s=\frac{4x-y^2}{4-y}
    t=\frac{4(y-x)}{4-y}
    u=\frac{8y-4x-y^2}{4(4-y)}
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  2. #2
    MHF Contributor
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    Quote Originally Posted by bugatti79 View Post
    Folks,

    I am struggling with this seemingly simple task of solving for s and t in terms of x and y to ultimately get u in terms of x and y.

    x=s+st/4+t^2/4 (1)
    y=s+t (2)
    u=s/4+t/2 (3)

    My attempt is as follows: From eqn 1 find t, its a quadratic in t
    t=\frac{-s+- \sqrt {s^2+4(4x-4s)}}{2} (4)

    From (2) find t t=y-s (5)

    Then equate 4 and 5???.... Im actually lost....

    The answers are

    s=\frac{4x-y^2}{4-y}
    t=\frac{4(y-x)}{4-y}
    u=\frac{8y-4x-y^2}{4(4-y)}
    From (2)

    t=y-s

    Substitute into (1)

    \displaystyle\ x=s+\frac{s(y-s)+(y-s)^2}{4}\Rightarrow\ 4x=4s+sy-s^2+y^2-2sy+s^2

    \Rightarrow\ 4x=y^2+s(4-y)

    from which "s" can be isolated.
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