Answer:
-2X1 + X2 + 2X3= -3
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Your matrix
№ X1 X2 X3 b
1 2 1 -1 8
2 -3 -1 2 -11
3 -2 1 2 3
Make the pivot in the 1st column by dividing the 1st row by 2
№ X1 X2 X3 b
1 1 1/2 -1/2 4
2 -3 -1 2 -11
3 -2 1 2 3
Eliminate the 1st column
№ X1 X2 X3 b
1 1 1/2 -1/2 4
2 0 1/2 1/2 1
3 0 2 1 11
Make the pivot in the 2nd column by dividing the 2nd row by 1/2
№ X1 X2 X3 b
1 1 1/2 -1/2 4
2 0 1 1 2
3 0 2 1 11
Eliminate the 2nd column
№ X1 X2 X3 b
1 1 0 -1 3
2 0 1 1 2
3 0 0 -1 7
Find the pivot in the 3rd column in the 3rd row (inversing the sign in the whole row)
№ X1 X2 X3 b
1 1 0 -1 3
2 0 1 1 2
3 0 0 1 -7
Eliminate the 3rd column
№ X1 X2 X3 b
1 1 0 0 -4
2 0 1 0 9
3 0 0 1 -7
Solution set:
x1 = -4
x2 = 9
x3 = -7
