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Math Help - 2 Equations - Don't know where to start

  1. #1
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    2 Equations - Don't know where to start

    Ok got 2 algbaric equations.
    Can someone help me here..... really really confused where to start.

    Here they are...
    0.8v + 0.54y -1.6z > 0

    where

    v + y + z = 1 (v,y or z cannot be <0)

    Help much appreciated

    Need value(s) for z only really, but if you can get the value(s) of y and v that would be nice too

    I did post this in the advanced section but looking at some others this looks basic in comparison so thoguht I might get a quicker response here!

    Many Thanks for your help

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  2. #2
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    Quote Originally Posted by BackBlood View Post
    Ok got 2 algbaric equations.
    Can someone help me here..... really really confused where to start.

    Here they are...
    (A) 0.8v + 0.54y -1.6z > 0

    where

    (B) v + y + z = 1 (v,y or z cannot be <0)

    Help much appreciated

    Need value(s) for z only really, but if you can get the value(s) of y and v that would be nice too

    I did post this in the advanced section but looking at some others this looks basic in comparison so thoguht I might get a quicker response here!

    Many Thanks for your help
    1. Solve (B) for v=-y-z+1

    2. Substitute v in (A) by -y-z+1:

    0.8(-y - z + 1) + 0.54y - 1.6z > 0

    3. Solve for z:

    (C) z<\dfrac{40-13y}{120}

    4. Since all three variables have to be positive

    40-13y>0~\implies~y<\dfrac{40}{13}

    Then
    0<z<\dfrac13 according to (C)

    and

    0<v<\dfrac23 according to (B)
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