Question 896268
2x + 3y + z = −1
3x + 3y + z = 1
2x + 4y + z = −2

2,3,1,-1
3,3,1,1
2,4,1,-2

divide row 1 by 2
1,3/2,1/2,-1/2
3,3,1,1
2,4,1,-2

add  down (-3) *row 1 to row 2
1,3/2,1/2,-1/2
0,-3/2,-1/2,5/2
2,4,1,-2

add  down (-2) *row 1 to row 3
1,3/2,1/2,-1/2
0,-3/2,-1/2,5/2
0,1,0,-1

divide row 2 by -3/2
1,3/2,1/2,-1/2
0,1,-2/-6,10/-6
0,1,0,-1

add  down (-1) *row 2 to row 3
1,3/2,1/2,-1/2
0,1,1/3,5/-3
0,0,-1/3,-2/-3

divide row 3 by -1/3
1,3/2,1/2,-1/2
0,1,1/3,5/-3
0,0,1,-2

We now have the value for the last variable.
We will work our way up and get the other solutions.

add up  (-1/3) *row 3 to row 2
1,3/2,1/2,-1/2
0,1,0,-1
0,0,1,-2

add up  (-1/2) *row 3 to row 1
1,6/4,0,2/4
0,1,0,-1
0,0,1,-2

add up  (-3/2) *row 2 to row 1
1,0,0,2
0,1,0,-1
0,0,1,-2

final
1,0,0,2
0,1,0,-1
0,0,1,-2

1,0,0,2
0,1,0,-1
0,0,1,-2
"2","-1","-2"
(2,-1,-2)

determinant  of
2,3,1
3,3,1
2,4,1
= 1

x = 2/1 = 2/1 = 2
y = -1/1 = -1/1 = -1
z = -2/1 = -2/1 = -2