Question 136221
I'll help you

You got the matrix [1   2   -1]
                   [2   1   -7]

Now we perform row operations basically to make the elements below and above the principal diagonal as 0

Consider R2 - 2 R1
So the matrix becomes   [1   2   -1]
                        [0  -3   -5]

Now the element below the diagonal became 0

To get the elemnts along the diagonal as 1,
we divide the R2 by -3

==>       [1   2   -1]
          [0   1   -5/-3]

=         [1   2    -1]
          [0   1    5/3]

Now to make the element above the diagonal 0, perform

R1 - 2 R2

==>       [1   0   -1-10/3]
          [0   1     5/3]

==>       [1   0    -13/3]
          [0   1      5/3]

This represents the original equation

Thus we get x = -13/3  and y = 5/3

These satisfy the given equation.

Hope it is clear

Good luck!!!

Dolly