100 points for correct answer

Step-by-step explanation:

Let the argumented matrix:

[ 3-1 +9]

[ 2+1 -4]

We solve the matrix by Gauss- Jordan Eleminating:

Let denote the above matrix like A.

Let the denote the row by 1 by R1 =[3 -1 | +9]

And let denote rhe row 2 by R2= [ 2 +1 | -4]

So, we will apply the elementary operations per row

First operation: R2=3 R2, then [-3 -9| 9]

[ 6 3| -72]

Second operation: R2 = R2/ 2

[ 3 -7| 9]

[ 3 3/2 | -6]

Now, R2 = R2 - R1

[3 -7| 9 ]

[0 5/2 | -15]

R2=R2÷(5/2), That is :

R1=R1/3

R1=R1+( 1/3) R2

That Is : + (1/3) R2

That is :

[1 0| 1]

[ 0 1| -6]

So the above- argumented matrix is equivalent to the following linear system of equations:

1x +0 y =1

0x+1y= -6

That is

x=1

y= -6

One solution for the matrix A is (1, -6)

The correct solution will be ( 1, -5)