# Solving non-linear and linear simultaneous equations with fsolve

Version 1.1.0.0 (1.46 KB) by
solvesimul.m solves non-linear and linear simultaneous equations.
Updated 27 Jan 2010

solvesimul.m can be easily adapted to solve more equations but as it stands it will solve 2 unknowns in 2 equations (1 non-linear and one linear).

To solve equations of this form...

a*x + b*y = A (1)
a1*x^2 + b1*y^2 = B (2)

...with fsolve (used by solvesimul.m) you need to rewrite them so that they equal zero.

so (1) and (2) become
a*x + b*y - A = 0 (1a)
a1*x^2 + b1*y^2 - B = 0 (2a)

then using a nested function approach (there are many other ways) you can solve some system of non-linear equations.
An example,

2*x + 3*y - 8 = 0
4*x^2 + 5*y^2 - 24 = 0

At the MATLAB command-line prompt you run the 'solvesimul' m-file function with the correct arguments
i.e. coefficients and constants in the equations in the appropriate order.
NB: please see final note below demo of the solvesimul command.

>> b=solvesimul(2,3,4,5,8,24);
1.0e-014 *

0
0.7105

>> b

b =

1.0000
2.0000

These are the solutions for the 2 equations i.e. x = 1, y=2.
----------------------------------------------------------------
The code I wrote for 'solvesimul' is attached. Save it to your working folder and run as above.
NB: you can use any one of the 3 fsolve formats by commenting out the other 2 you don't need in the attached m-file code.

Important:
You need to enter the args (i.e equation coefficients) to solvesimul.m in the order they appear in the equations with equation constants specified last in the correct order.

### Cite As

Bruce Raine (2024). Solving non-linear and linear simultaneous equations with fsolve (https://www.mathworks.com/matlabcentral/fileexchange/26259-solving-non-linear-and-linear-simultaneous-equations-with-fsolve), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R2009b
Compatible with any release
##### Platform Compatibility
Windows macOS Linux
##### Categories
Find more on Nonlinear Optimization in Help Center and MATLAB Answers