# 5 equations, 5 unknowns using fsolve; with scientific variables

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##### 3 Comments

Walter Roberson
on 26 Nov 2023

John D'Errico
on 26 Nov 2023

It is just as easy to paste in actual text, instead of a picture of your code. I will assert that is is going to take some effort to copy your code line by line, and get a valid copy. So that means the set of people willing to help you will be small.

Is there a good reason why you want to make it more difficult to get help?

### Answers (1)

David Goodmanson
on 27 Nov 2023

Edited: David Goodmanson
on 27 Nov 2023

Hi Kaushal,

looks like 6 eqns 6 unknowns not 5. All of your unknowns appear in the numerators of the given expressions and no products of unknowns occur, so it looks like a set of linear equations which is easy to solve. Whether they are long or short I don't think it helps comprehension to have variables full of underlines; for example in a set of equations, I think T2 is easier to read than T_2 and I will use tfoA in place of t_fluid_outlet_ATPS. The the six equations have the form (t involves less keyboard strokes than T)

(ts1 -t2)*c1 -q = 0

(t2 -tavg)*c2 -q = 0

c3 + q*c4 - tavg = 0

(tavg -t3)*c5 -q = 0

(t3 -t4)*c6 -q = 0

c7*(tfoA -c8) -q = 0

where the constants are various combinations of known quantities that you can calculate.

If you create a column vector of unknowns with

X = [q t2; t3; t4; tavg; tfoA] % semicolons create a column vector

and a column vector of all the known constant terms put over to the right hand side where the zeros are:

Y = [-c1*ts1; 0; -c3; 0; 0; c7*c8]

then this can be put into matrix multiplication form

MX = Y with

[-1 -c1 0 0 0 0 [q] [-c1*ts1]

-1 c2 0 0 -c2 0 [t2] [0 ]

M = c4 0 0 0 -1 0 x [t3] = [-c3 ]

-1 0 -c5 c5 0 0 [t4] [0 ]

-1 0 c6 -c6 0 0 [tavg] [0 ]

-1 0 0 0 0 c7] [tfoA] [c7*c8 ]

You can pretty much read off the six eqns.

The solution to MX = Y is found with the backslash command.

##### 1 Comment

Walter Roberson
on 27 Nov 2023

Personally, I have gotten into the habit of using underscores more because when I am using symbolic variables in LiveScript (or here on MATLAB Answers) then the underscores and what follows are processed to render as subscripts or superscripts or accents.

syms a a_2 a__2 a_bar a__bar a_dot a__dot a_ddot a__ddot

[a a_2 a__2 a_bar a__bar a_dot a__dot a_ddot a__ddot]

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