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Thread: A problem dealing with a graph, turning the graph into a system of equations, solve

  1. #1
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    A problem dealing with a graph, turning the graph into a system of equations, solve


    https://gyazo.com/540d819fa8a14cbccdbd2b43791a5a80

    I really just need some guidance on part (a), because I don't really know how to turn that into a system.
    If I had to guess I would solve for each variable but that would only give me 3 equations.
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  2. #2
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    Re: A problem dealing with a graph, turning the graph into a system of equations, sol

    $$b = \dfrac{1}{2}(a+10)$$

    $$c = \dfrac{1}{3}(a+b+60)$$

    $$d = \dfrac{1}{2}(b+c)$$

    $$30 = \dfrac{1}{2}(c+d)$$
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  3. #3
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    Re: A problem dealing with a graph, turning the graph into a system of equations, sol

    Quote Originally Posted by MrJank View Post

    https://gyazo.com/540d819fa8a14cbccdbd2b43791a5a80

    I really just need some guidance on part (a), because I don't really know how to turn that into a system.
    If I had to guess I would solve for each variable but that would only give me 3 equations.
    There are 4 unknowns (a,b,c,d) so you will need 4 equations if you want to solve them.
    Look at Lake b: What lakes are upstream of it? What is the average of the salinity of these upstream lakes?
    Look at Lake d: Do the same.
    Look at Lake 30: Do the same.
    This will give you three more equations - they've given you the other one.

    Come back if you need help after you've tried that.
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  4. #4
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    Re: A problem dealing with a graph, turning the graph into a system of equations, sol

    Quote Originally Posted by SlipEternal View Post
    $$b = \dfrac{1}{2}(a+10)$$

    $$c = \dfrac{1}{3}(a+b+60)$$

    $$d = \dfrac{1}{2}(b+c)$$

    $$30 = \dfrac{1}{2}(c+d)$$
    Or (directly from these equations)
    a- 2b= -10
    a+ b- 3c= -60
    b+ c- 2d= 0
    c+ d= 60.

    You might find that form easier to work with.
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