Let the number of nickels be x
Let the number of dimes be y


                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
nickels       x      $0.05     $0.05x
dimes         y      $0.10     $0.10y
-------------------------------------------
TOTALS       57      -----     $3.95

 The first equation comes from the "Number of coins"
 column.

  

                  x + y = 57

 The second equation comes from the last column.
  

           0.05x + 0.10y = 3.95

Get rid of decimals by multiplying every term by 100:

               5x + 10y = 395

 So we have the system of equations:
           .

We solve by substitution.  Solve the first equation for y:

           x + y = 57
               y = 57 - x

Substitute (57 - x) for y in 5x + 10y = 395

    5x + 10(57 - x) = 395
     5x + 570 - 10x = 395
          -5x + 570 = 395
                -5x = -175
                  x = 35 = the number of nickels.

Substitute in y = 57 - x
              y = 57 - (35
              y = 22 dimes.


Checking:  35 nickels is $1.75 and 22 dimes is $2.20
            That's 57 coins.
            And indeed $1.75 + $2.20 = $3.95
Edwin