Can this be done algebraically?

Question

A cashier has 20 coins consisting of nickels, dimes, and quarters with a value of $2.65. If the number of dimes is three less than the number of nickels, how many of each type of coin does she have?

Answer 1

Arranging a matrix solution with N nickles, D dimes and Q quarters:

N + D + Q = 20

.05N + .10D + .25Q = 2.65

N - D +0Q = 3

The 3x4 matrix is:

1 1 1 20

.05 .10 . 25 2.65

0 1 1 3

And the RREF solution is N=8, D= 5, Q= 7