# Conversion of linear equations to form Ax=b

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Hello everyone,

I have the following equations:

syms t u v w x y z

intersection_a = -t + w + x == 100;

intersection_b = t - u == 100;

intersection_c = v + w - y - z == 0;

intersection_d = u + v == 40;

I can convert it to form of Ax=b using equationsToMatrix(). But my question is if I have t = 100 and w+x+y = 100, then does the equation change? Do I need to put t = 100 etc in these equations? If I will, then there will be no t in equations. How I will be able to write then it in form of Ax= b where x = [t u v w x y z] '?

Thanks in advance.

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### Accepted Answer

Sam Chak
on 15 Sep 2022

You have only 4 equations, but there are 6 unknowns. So, the linear system is clearly rank-deficient.

syms t u v w x y z

t = 100;

intersections = [-t + w + x == 100, ...

t - u == 100, ...

v + w - y - z == 0, ...

u + v == 40];

vars = [u, v, w, x, y, z];

[A, b] = equationsToMatrix(intersections, vars)

x = linsolve(A, b)

##### 6 Comments

Torsten
on 15 Sep 2022

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