Question 891216
Against my better judgement, I will do two for you.
3x + 3y + z = 22
x + z = 6
4y + 3z = 8 

3,3,1,22
1,0,1,6
0,4,3,8

divide row 1 by 3/1
1,1,1/3,22/3
1,0,1,6
0,4,3,8

add  down (-1/1) *row 1 to row 2
1,1,1/3,22/3
0,-1,2/3,-4/3
0,4,3,8

add  down (0/1) *row 1 to row 3
1,1,1/3,22/3
0,-1,2/3,-4/3
0,4,3,8

divide row 2 by -1/1
1,1,1/3,22/3
0,1,2/-3,-4/-3
0,4,3,8

add  down (-4/1) *row 2 to row 3
1,1,1/3,22/3
0,1,2/-3,4/3
0,0,-17/-3,8/3

divide row 3 by 17/3
1,1,1/3,22/3
0,1,2/-3,4/3
0,0,1,24/51

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

add up  (-2/-3) *row 3 to row 2
1,1,1/3,22/3
0,1,0,-252/-153
0,0,1,8/17

add up  (-1/3) *row 3 to row 1
1,1,0,1098/153
0,1,0,28/17
0,0,1,8/17

add up  (-1/1) *row 2 to row 1
1,0,0,1598/289
0,1,0,28/17
0,0,1,8/17

final
1,0,0,94/17 = 5.52941176
0,1,0,28/17 = 1.64705882
0,0,1,8/17 = 0.47058824

"94/17","28/17","8/17"


next one
2x + 5y - 2z = 14
5x - 6y + 2z = 0
4x - y + 3z = -7 

2,5,-2,14
5,-6,2,0
4,-1,3,-7

divide row 1 by 2/1
1,5/2,-1,7
5,-6,2,0
4,-1,3,-7

add  down (-5/1) *row 1 to row 2
1,5/2,-1,7
0,-37/2,7,-35
4,-1,3,-7

add  down (-4/1) *row 1 to row 3
1,5/2,-1,7
0,-37/2,7,-35
0,-11,7,-35

divide row 2 by -37/2
1,5/2,-1,7
0,1,14/-37,-70/-37
0,-11,7,-35

add  down (11/1) *row 2 to row 3
1,5/2,-1,7
0,1,14/-37,70/37
0,0,-105/-37,-525/37

divide row 3 by 105/37
1,5/2,-1,7
0,1,14/-37,70/37
0,0,1,-5

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

add up  (-14/-37) *row 3 to row 2
1,5/2,-1,7
0,1,0,0
0,0,1,-5

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

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

final
1,0,0,2
0,1,0,0
0,0,1,-5

(2,0,-5)