General Solution To Three Simultaneous Equations

4 replies · 4K views · last reply
DavidZuccaro
Messages
15
Reaction score
0
I herewith submit for reference, review and comment the general solution to 3 simultaneous equations as follows:

Handwritten-style algebra deriving y from three linear equations by successive substitution, ending with c2 b3/b1 - c2 b2 a3/(a1 b1) - c3 = y(c1 + c2 b2 a2/(a1 b1)).

Handwritten-style algebra showing successive substitution steps deriving a general expression for y and z in terms of a, b and c coefficients, with equation numbers (6) and (5) marked.

Handwritten-style algebra derivation solving three simultaneous equations for z and x, with numbered steps and references to equations (4), (6), (7) and (8), ending in a general expression for x in terms of coefficients a, b and c.
 
Lot of work plus a lot of typesetting !
I do notice that you have written down a general solution for a not so general set of three equations in three unknowns.
Are you familiar with things like inverting a 3x3 matrix? Your matrix has zeros on the diagonal.
 
  • Like
Likes   Reactions: DavidZuccaro
BvU said:
Lot of work plus a lot of typesetting !
I do notice that you have written down a general solution for a not so general set of three equations in three unknowns.
Are you familiar with things like inverting a 3x3 matrix? Your matrix has zeros on the diagonal.

I agree, it's a general solution to a specific set of equations :)

Thanks, I thought that there was a simpler way of solving those.
 
The typesetting was not a problem -- all handled by LibreOffice Math. It was easier than writing.