Question 890347
n+6=d
2q+1=n
25q+10d+5n=460

1d-1n+0q=6
0d+1n-2q=1
10d+5n+25q=460

1,-1,0,6
0,1,-2,1
10,5,25,460

1,-1,0,6
0,1,-2,1
10,5,25,460

add  down (0/1) *row 1 to row 2
1,-1,0,6
0,1,-2,1
10,5,25,460

add  down (-10/1) *row 1 to row 3
1,-1,0,6
0,1,-2,1
0,15,25,400

divide row 2 by 1/1
1,-1,0,6
0,1,-2,1
0,15,25,400

add  down (-15/1) *row 2 to row 3
1,-1,0,6
0,1,-2,1
0,0,55,385

divide row 3 by 55/1
1,-1,0,6
0,1,-2,1
0,0,1,7

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

add up  (2/1) *row 3 to row 2
1,-1,0,6
0,1,0,15
0,0,1,7

add up  (0/1) *row 3 to row 1
1,-1,0,6
0,1,0,15
0,0,1,7

add up  (1/1) *row 2 to row 1
1,0,0,21
0,1,0,15
0,0,1,7

final
1,0,0,21 dimes
0,1,0,15 nickels
0,0,1,7 quarters

210+075+175=460