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Math Help - System of four linear equations

  1. #1
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    System of four linear equations

    Hi all, having trouble organising this into a system of linear equations: A family has 4 pets. A dog called abel and 3 cats called bella, caleb and diago. Abel weighs as much as the cats all together. Bella is the average weight of the other two cats. caleb weighs twice as much as diago. Without the smallest animal, the other three weigh 28kg together. how can i write this as a system of four linear equations
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  2. #2
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    Would the equations be:
    a = 3b + 3c + 3d
    b = c/2 + d/2
    c = 2d
    a + b + c = 28
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  3. #3
    Member kjchauhan's Avatar
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    Let x_{1}=weight of Abel
    x_{2}=weight of Bella
    x_{3}=weight of Cabel
    x_{4} =weight of Diago

    Then equations::

    x_{1} - (x_{2}+x_{3}+x_{4})=0
    2x_{2}-(x_{3}+x_{4})=0
    x_{3}-2x_{4}=0
    x_{1}+x_{2}+x_{3}=28
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  4. #4
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    I would use the coefficient matrix to solve the system:

    \displaystyle\begin{bmatrix}1&-1&-1&-1&:0\\0&2&-1&-1&:0\\0&0&1&-2&:0\\1&1&1&0&:28\end{bmatrix}
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  5. #5
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    Quote Originally Posted by Oiler View Post
    Would the equations be:
    a = 3b + 3c + 3d
    b = c/2 + d/2
    c = 2d
    a + b + c = 28
    Yout 1st one should be a = b + c + d ; anyhow:

    Since c = 2d:
    a - b - 3d = 0
    a + b + 2d = 28
    2b - 3d = 0

    Easily solved...
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