Question 891813
What is included in a two course meal? 
starts and main?
main and dessert?
Under these circumstances we have three unknowns and three equations
w= three course
x= starters and main
y= main and dessert

w+x+0*y=10
w+0*x+y=8
w+x+y=12

1,1,0,10
1,0,1,8
1,1,1,12

add  down (-1/1) *row 1 to row 2
1,1,0,10
0,-1,1,-2
1,1,1,12

add  down (-1/1) *row 1 to row 3
1,1,0,10
0,-1,1,-2
0,0,1,2

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

add  down (0/1) *row 2 to row 3
1,1,0,10
0,1,-1,2
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  (1/1) *row 3 to row 2
1,1,0,10
0,1,0,4
0,0,1,2

add up  (0/1) *row 3 to row 1
1,1,0,10
0,1,0,4
0,0,1,2

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

final
1,0,0,6
0,1,0,4
0,0,1,2

6 three course 
4 starters and main
2 main and dessert
10 starters
12 main
8 dessert

"6","4","2"
(6,4,2)