IF there is a linear system such as :


I want a way of solving this problem different from Gaussian-Jordan method

I tried the elimination method but it didn't work with me (even though I rearranged the equations and tried solving this problem by this way several times but the answer was wrong ) I don't know if I made mistakes or this way can't go further with this kind of system


  • $\begingroup$ Why don't you show what you've done so far? At least, writing it as an augmented matrix or equivalently, matrix*vector = vector. $\endgroup$
    – Batman
    Commented May 15, 2014 at 2:06

1 Answer 1


Substitute the third equation into the 1st and 2nd: $$ y=-2x+1-2x+2y \quad \quad x=-2y-x+y+2 $$ $$ y=4x-1 \quad \quad y=2-2x $$

Equating the 2 equations you get: $$ 4x-1=2-2x $$ so $x=1/2$. Then $y=1$ and $z=-1/2$

  • $\begingroup$ good idea ! is it working with all kinds of linear systems of 3 variables ? $\endgroup$
    – Maher
    Commented May 15, 2014 at 21:33
  • $\begingroup$ This is a standard and simple way of dealing with linear systems and for a 3x3 linear system the calculations are easy in general. $\endgroup$
    – Kal S.
    Commented May 15, 2014 at 22:09

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