# How to solve 5 equations with 5 unknowns

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Hinko Fic on 29 May 2015
Answered: Alex Sha on 12 Oct 2019
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
Roger Stafford on 11 Mar 2018
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.

Roger Stafford on 29 May 2015
Edited: Roger Stafford on 29 May 2015
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 on 30 May 2015
That works, ty a lot, you saved me a lot of time

Alex Sha on 12 Oct 2019
Numercial solution:
a: 9.00473933649289
b: 1.18483412322275
c: 3.55450236966825
d: 1.54545454545455
e: 17.2

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