Multiple equations with relations !

[taracus]

I'm very bad at math so please correct me or let me know if I'm posting in the wrong section.

I have a set of equations (in reality any number > 2) but if its solvable for 3 it would be good enough.
Si * Xi - Ri+Yi = C where i=0...n (or 3) and Si and Ri are unknown BUT I know:
Rj = SUM(Si) i=0->n AND i != j

That is Ri == Sum of all S except the Si.

Now I would need help (if its even possible?) to solve the equation so I have a formula to calculate S for any given i (all Xs and Ys are known and C is known and constant for all equations).

Any help or if you could point me in the right direction I would appreciate it.
Or if the something is missing for the equation to be solvable please let me know.

BR Tomas A

 

[JeffM]

I'm very bad at math so please correct me or let me know if I'm posting in the wrong section.

I have a set of equations (in reality any number > 2) but if its solvable for 3 it would be good enough.
Si * Xi - Ri+Yi = C where i=0...n (or 3) and Si and Ri are unknown BUT I know:
Rj = SUM(Si) i=0->n AND i != j

That is Ri == Sum of all S except the Si.

Now I would need help (if its even possible?) to solve the equation so I have a formula to calculate S for any given i (all Xs and Ys are known and C is known and constant for all equations).

Any help or if you could point me in the right direction I would appreciate it.
Or if the something is missing for the equation to be solvable please let me know.

BR Tomas A

You did not say what course you are studying. It would help a lot to know that. Even if you are studying linear algebra, the general case for n > 2 looks to me to be messy. If you know no linear algebra, it is feasible to attack the problem using elementary algebra if n = 3.

If n = 3, you can simplify by eliminating the indices and reducing certain expressions.

\(\displaystyle Let\ e = x_1,\ f = x_2,\ g = x_2, a = c_1 - y_1,\ b = c_2 - y_2,\ d = c_3 - y_3,\ s_1 = t,\ s_2 = u,\ and\ s_3 = v.\)

e, f, g, a, b, and d are constants.

\(\displaystyle So\ r_1 = u + v, r_2 = t + v,\ and\ r_3 = t + u.\)

So your 3 equations simplify to:

\(\displaystyle et - u - v = a.\)

\(\displaystyle fu - t - v = b.\)

\(\displaystyle gv - t - u = d.\)

Do you know how to solve three simultaneous linear equations in three unknowns? If not, why in the world would this problem be assigned?

Can you at least start and show us how far you can go?