Solution of the system of equations 2𝑥+𝑦=3,𝑥−2𝑦=−12x+y=3,x−2y=−1 by Gauss elimination method area)𝑥=1,𝑦=2x=1,y=2b)𝑥=1,𝑦=1x=1,y=1c)𝑥=1,𝑦=−1x=1,y=−1d)𝑥=−1,𝑦=1x=−1,y=1

It seems like there's a bit of confusion in your question as the equations and options are not clearly stated. However, I'll guide you on how to solve a system of equations using the Gauss elimination method.

Let's take the system of equations as:

1. 2x + y = 3
2. x - 2y = -1

Step 1: Write the system of equations in matrix form. The matrix is:

[2  1 | 3]
[1 -2 | -1]

Step 2: Swap row 1 and row 2 to get the larger pivot in the top left. The matrix becomes:

[1 -2 | -1]
[2  1 | 3]

Step 3: Subtract 2 times the first row from the second row to eliminate x from the second equation. The matrix becomes:

[1 -2 | -1]
[0  5 | 5]

Step 4: Divide the second row by 5 to make the coefficient of y equal to 1. The matrix becomes:

[1 -2 | -1]
[0  1 | 1]

Step 5: Add 2 times the second row to the first row to eliminate y from the first equation. The matrix becomes:

[1 0 | 1]
[0 1 | 1]

So, the solution to the system of equations is x = 1, y = 1. Therefore, the correct option is b) x=1, y=1.