Algorithm For Solving Systems Of Linear Equations

First, you have to know how to solve it manually.  Once you know that, then constructing an algorithm is easy.

The algorithm is as follows.


prompt for the coefficient (a for X**2, b for X , and, c for constant).
Find the discriminant D.

D = b**2 - 4.*a*c

IF D == 0 THEN
X has repeated root.
root = - b / 2.*a

ELSE IF D > 0. THEN
X has two distinct roots
root_1 = (- b + SQRT (b**2 - 4*a*c)) / 2.*a
root_2 = (- b -  SQRT (b**2 - 4*a*c)) / 2.*a

ELSE
X has complex root.
root_1 = -b / 2*a + SQRT (D) i / 2*a
root_2 = -b / 2*a  - SQRT (D) i / 2*a

okunade, the solution you presented is for solving a single quadratic equation.  Not applicable here.

You went too far. It's the Guassian elimination method (either through backsolving or elementary row operations).

An example of a  non-homogeneous system of linear equation with 3 unknowns is:

2x + 3y - 5z = 2
4x - y + 2z =  6
x  + z -  4z = 4

@ishmael
Yes you're right, (they are numerical methods of solving linear equations)and i think they're the methods, best suited for the problem.

I developed some C programs when i was in school to solve the exact same thing ,  Its been ages since i've seen the programs ,

The methods are very programmable, as opposed to the plain Gaussian methods ,

I'd recommend the book ,numerical recipes in C, a copy and paste solution should be there
http://www.nr.com/oldverswitcher.html 

you can either use numerical solution or matix method to solve the probelm. But whichever method you choose, you can solve the problem by examinig how to solve the problem with pen and paper first. Then you can formulate the algorithm. Or better still, you can check numerical methods texts. Most Numerical method text feature algoriths.