In forward elimination, we want to obtain a 0 in the a21 position. To accomplish this, we can alter the second line in the matrix by subtracting from it 2 * the first row.
In this way we would write this ERO as:
Now, placing it back in the matrix equation form:
It says that the second equation is now -2x2 = 2 therefore x2 = -1. Now put it into the first equation:
x1 + 2(-1) = 2, and hence x1 = 4.
This is known as the back-substitution.