Gauss Elimination Method
The Gauss elimination method is to transform a system of equations into an equivalent system that is in triangular form.
To facilitate the calculation, transform the system into a matrix and place the coefficients of the variables and the independent terms into the matrix (separated by a straight line).
|x||+ y||- z||=||1|
Change the position of row 3 to where row 1 is and shift the other rows down accordingly:
Subtract row 2 by three times the value of row 1 and subtract row 3 by five times the value of row 1.
Subtract row 3 by twice the value of row 2.