How do I combine equations for absolute independent motion with pulleys?

[JustDerek]

Homework Statement

I've been given a problem with pulleys which I have attached to this post. I've derived the equations shown in the post but I'll also write them below. What I'm struggling with is how to combine them.

Homework Equations

##l_1=S_a+2S_c##
##l_2=S_d+(S_d-S_c)##
##l_3=S_e+(S_e-S_c)##

In a similar example I've been given but with less pulleys it shows :
##l_1+l_2=S_a+4S_d##
This is the part I don't get. I don't get how the two equations combine to become that and I'm sure if I can understand that I can finish the rest.

The Attempt at a Solution

 

[mfb]

You can add the equations in any way you want. Something that gets rid of S_c and S_d is probably useful.

As an example, you have "+2 S_c" in the first equation and "-S_c" in the second one. You can multiply the second equation (both sides!) with two, then add the two equations.

 

[Merlin3189]

I'm not sure why you are trying to find ##l_1, l_2\ and\ l_3##. There is no absolute value for them. Changing the length of any of them does not affect the velocity ratio nor the forces.
What I think you need to know are the velocity ratios and the force ratios, which you should be able to do by inspection in a simple example like this.
I would suggest the way to deal with the forces is to label one of them F or whatever, then write the others as multiples (or fractions.)

 

[JustDerek]

Managed to get there myself eventually but thanks for the intended help