How to solve 5 equations with 5 unknowns

Hi, I don't have any idea how to solve this system. I'm beginner so i don't knew how to write corect code. Pls help me. Equations:

(A-B-C)*5=C*6 ////
(A-B-C)*2+B*3=(A-B)*D ////
(A-B)*(2-D)=B*3 ////
(A-B)*2+B*4=B*E ////
A*2+(A-B)*3+(A-B-C)*2=50

[Muhammad Usman Saleem]

use this http://math.stackexchange.com/questions/255750/5-linear-equations-in-5-unknowns and to solve 5 equations with 5 unknown variables use this http://math.cowpi.com/systemsolver/5x5.html hope this is fine...

[Roger Stafford]

Not all these equations are linear.

[Muhammad Usman Saleem]

@Roger check the equations again..

[John D'Errico]

Oh, gosh. I learn something new every day. Apparently (A-B)*D, (A-B)*(2-D), and B*E are all linear in the unknowns! I guess I'll need to go back and review my notes for all of those linear algebra classes. Darn this new math.

[Walter Roberson]

Muhammad, the expressions involve A*D, B*D, and B*E, so they certainly are non-linear.

[Hinko Fic]

Yeah, i knew how to solve linear, but this isn't. That's reason why i need help. I need to solve these equations with different numbers (more complicated) for my project in school

[Roger Stafford]

I don't remember this problem from almost two years ago, but apparently all of us (except perhaps Muhammad Saleem) overlooked the fact that it is actually a system of five linear equations in the five unknown quantities, A, B, C, d=(A-B)*D, and e=B*E, so it can be solved for these latter five variables using matrix division. From those solutions, it is easy to then find D and E: D = d/(A-B) and E = e/B.

Answer 1

[Roger Stafford]

You can use 'solve' in the Symbolic Toolbox to solve them.

My alternate method was in error. Just use 'solve'. It does very well.

[Hinko Fic]

I used this code:

equ1='(a-b-c)*5-6*c' ////
equ2='(a-b-c)*2+b*3-(a-b)*d' ////
equ3='(a-b)*(2-d)-b*3' ////
equ4='(a-b)*2+b*4-b*e' ////
equ5='a*2+(a-b)*3+(a-b-c)*2-50' ////
sol=solve(equ1,equ2,equ3,equ4,equ5) ////

but now i don't knew how to transform my results into numerical because i got "a: [1x1 sym]...

[Muhammad Usman Saleem]

solve by substitution and simultaneously methods to make this in 1*1 system

[Muhammad Usman Saleem]

(1) firstly you have to make a function that take these 5 equations as input (2) make an algorithm by using methods of simultaneously or substitutions.. (3) set output of this function as system of 1*1 equation..

[Walter Roberson]

structfun(@double, sol, 'Uniform', 0)

will return back a structure whose fields are a, b, c, d, e. For any particular one of them you can use (e.g.) double(sol.b)

[Hinko Fic]

That works, ty a lot, you saved me a lot of time

Answer 2

[Alex Sha]

Numercial solution:

a: 9.00473933649289

b: 1.18483412322275

c: 3.55450236966825

d: 1.54545454545455

e: 17.2