Question 901781
5*n+10*d+25*q=2190
n+d+q=125
2*d=n
n-2*d=0

5,10,25,2190
1,1,1,125
1,-2,0,0

5,10,25,2190
1,1,1,125
1,-2,0,0

divide row 1 by 5
1,2,5,438
1,1,1,125
1,-2,0,0

add  down (-1) *row 1 to row 2
1,2,5,438
0,-1,-4,-313
1,-2,0,0

add  down (-1) *row 1 to row 3
1,2,5,438
0,-1,-4,-313
0,-4,-5,-438

divide row 2 by -1
1,2,5,438
0,1,4,313
0,-4,-5,-438

add  down (4) *row 2 to row 3
1,2,5,438
0,1,4,313
0,0,11,814

divide row 3 by 11
1,2,5,438
0,1,4,313
0,0,1,74

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

add up  (-4) *row 3 to row 2
1,2,5,438
0,1,0,17
0,0,1,74

add up  (-5) *row 3 to row 1
1,2,0,68
0,1,0,17
0,0,1,74

add up  (-2) *row 2 to row 1
1,0,0,34
0,1,0,17
0,0,1,74

final
1,0,0,34
0,1,0,17
0,0,1,74

"34","17","74"
(34,17,74)
34n 17d 74q