




If we have one equation in three variables, and it is 3x + 4y  2z = 7 we can rearrange it to
x = (4/3) y + (2/3)z + 7/3,
or if we prefer, to
z = 2y + (3/2)x  7/2
We can change the coefficient matrix from its original form (3, 4, 2 ; 7),
with the notation that ; separates left and right side of the equation to any
one of (1, 4/3, 2/3; 7/3), (3/4,1, 1/2; 7/4), or (3/2, 2, 1; 7/2).
If there is a second equation we can subtract an appropriate multiple of our
first row to make the coefficient under the 1 into a zero; and so on.