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

1. ## 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.

2. ## Re: A problem dealing with a graph, turning the graph into a system of equations, sol

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

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

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

$$30 = \dfrac{1}{2}(c+d)$$

3. ## Re: A problem dealing with a graph, turning the graph into a system of equations, sol Originally Posted by MrJank  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.

4. ## Re: A problem dealing with a graph, turning the graph into a system of equations, sol Originally Posted by SlipEternal $$b = \dfrac{1}{2}(a+10)$$

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

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

$$30 = \dfrac{1}{2}(c+d)$$
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.