# Conversion of linear equations to form Ax=b

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aliza mustafa on 15 Sep 2022
Edited: Torsten on 15 Sep 2022
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)
A =
b =
x = linsolve(A, b)
Warning: Solution is not unique because the system is rank-deficient.
x =
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aliza mustafa on 15 Sep 2022
Thanks for sharing about solve() function. Can you please suggest me that is it alright to add w + y + z = 100 as an equation in intersections[] ?
Torsten on 15 Sep 2022
If it has to be satisfied, it has to be included. Why do you ask for this specific equation ? Is it different from the others ?

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