# How to solve this simple system of 2 equation in MATLAB

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Hi All;

I wonder if Matlab can solve this two equations to find the Fx and Fy as a function in the other constants. I know I can do it by hand just want to validate. Please see the initial code below

syms D L COST SINT Fx Fy

Fx * COST + Fy *SINT - D =0;

Fx * SINT + Fy * COST -L =0;

solve ( text: the two equations for Fx and Fy)

Thank you for your valuable suggestion

Aziz

##### 0 Comments

### Accepted Answer

John BG
on 6 May 2018

Edited: John BG
on 6 May 2018

Hi Abdulaziz

syms v Fx Fy D L

b=[D ;L]

b =

D

L

A=[(1-v^2)^.5 v;v (1-v^2)^.5]

A =

[ (1 - v^2)^(1/2), v]

[ v, (1 - v^2)^(1/2)]

F=A\b

=

(D*v^2 - D + L*v*(1 - v^2)^(1/2))/((1 - v^2)^(1/2)*(2*v^2 - 1))

(D*v - L*(1 - v^2)^(1/2))/(2*v^2 - 1)

.

these are the expressions

.

Fx=F(1)

=

(D*v^2 - D + L*v*(1 - v^2)^(1/2))/((1 - v^2)^(1/2)*(2*v^2 - 1))

Fy=F(2)

Fy =

(D*v - L*(1 - v^2)^(1/2))/(2*v^2 - 1)

.

with

v=sin(t)

.

if you find this answer useful would you please be so kind to consider marking my answer as Accepted Answer?

To any other reader, if you find this answer useful please consider clicking on the thumbs-up vote link

thanks in advance for time and attention

John BG

##### 0 Comments

### More Answers (2)

Stephan
on 4 May 2018

Edited: Stephan
on 4 May 2018

Hi,

you could do so:

% declare syms

syms D L t;

% Coefficient Matrix

A = [cos(t) sin(t); sin(t) cos(t)];

% RHS

b = [D ; L];

% Unknown: Fx, Fy

F = A\b;

% create Matlab function

fun = matlabFunction(F);

% Test for D = 0, L = -1 and t = pi()

D = 0;

L = -1;

t = pi();

[F] = fun(D, L, t)

this gives you a vector F containing Fx and Fy:

F =

0.0000

1.0000

or you do the same in a live script with symbolic toolbox and get the same result but nice:

Best regards

Stephan

##### 4 Comments

John BG
on 7 May 2018

Abdulaziz Abutunis
on 7 May 2018

##### 1 Comment

John BG
on 10 May 2018

Thanks Abdulaziz

feel free to ask me about having a look at any other particular question that you may consider I would be able to assist with.

Regards

John BG

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