# Software for Solving System of 8 Simultaneous Equations

#### djbayko

##### Member
SoSH Member
Does anyone know of any free software that is powerful enough to solve a system of 8 equations and 8 unknowns? Alternatively, does anyone have any paid software that can do it for me? This is a one-time need. All of the installable / online solvers that I've used in the past can only handle up to 6 equations.

Equations:
p=R_1*M_1-R_1
p=R_2*M_2-R_2
p=R_3*M_3-R_3
p=R_4*M_4-R_4
p=R_5*M_5-R_5
p=R_6*M_6-R_6
p=R_7*M_7-R_7
p=R_8*M_8-R_8
R_1+R_2+R_3+R_4+R_5+R_6+R_7+R_8=S

Looking to Solve For:
p
R_1
R_2
R_3
R_4
R_5
R_6
R_7
R_8

SoSH Member

#### swiftaw

##### Member
SoSH Member
Will wolframalpha do it?

#### djbayko

##### Member
SoSH Member
GNU Octave is free and could solve all your linear systems.

https://www.gnu.org/software/octave/
Thanks. I already found Octave, but I was having trouble translating my equations into the matrix format required by the program. I guess the software I've used in the past allowed you to paste in the equations as-is, and it would interpret them for you.

#### swiftaw

##### Member
SoSH Member
Although, looking this, it should be easily solvable by hand (if I’m reading it right).

You have that R_i = p/(M_i-1) for i=1,...,8

Let C_i =1/(M_i - 1)

So you have C_1*p + C_2*p + ... + C_8*p = S

So p = S/(C_1 + ... + C_8)

Which you can then plug into the first equation to find the R’s

#### Mr. Wednesday

##### Well-Known Member
SoSH Member
If you don't mind writing out the matrices, Excel has matrix multiply and matrix inverse functions, so you could use that too.

#### djbayko

##### Member
SoSH Member
Although, looking this, it should be easily solvable by hand (if I’m reading it right).

You have that R_i = p/(M_i-1) for i=1,...,8

Let C_i =1/(M_i - 1)

So you have C_1*p + C_2*p + ... + C_8*p = S

So p = S/(C_1 + ... + C_8)

Which you can then plug into the first equation to find the R’s
Brilliant!

Thank you so much. Now I can stop watching these math software tutorials #### Capnswill

##### Member
SoSH Member
Thanks. I already found Octave, but I was having trouble translating my equations into the matrix format required by the program. I guess the software I've used in the past allowed you to paste in the equations as-is, and it would interpret them for you.

This ought to work in octave, obviously don't set M_1 .. M_8 as rand though

M_1 = rand(1);
M_2 = rand(1);
M_3 = rand(1);
M_4 = rand(1);
M_5 = rand(1);
M_6 = rand(1);
M_7 = rand(1);
M_8 = rand(1);
S = rand(1);

A = [[diag([M_1-1,M_2-1,M_3-1,M_4-1,M_5-1,M_6-1,M_7-1,M_8-1]),-ones(8,1)];[ones(1,8),0]];
b = [zeros(8,1); S];

soln = A \ b;
R_1 = soln(1)
R_2 = soln(2)
R_3 = soln(3)
R_4 = soln(4)
R_5 = soln(5)
R_6 = soln(6)
R_7 = soln(7)
R_8 = soln(8)
p = soln(9)

Though solving by hand also works.