Let the number of nickles be x
Let the number of pennies be y


                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
nickles       x      $0.05     $0.05x
pennies       y      $0.01     $0.01y
-------------------------------------------
TOTALS       56      -----     $1.52

 The first equation comes from the second column.

  
                 x + y = 56

 The second equation comes from the last column.
  

           0.05x + 0.01y = 1.52

Get rid of decimals by multiplying every term by 100:

                 5x + 1y = 152

 So we have the system of equations:
           .

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

           x + y = 56
               y = 56 - x

Substitute (56 - x) for y in 5x + 1y = 152

  5x + 1(56 - x) = 152
    5x + 56 - 1x = 152
         4x + 56 = 152
              4x = 96
               x = 24 = the number of nickles.

 Substitute in y = 56 - x
               y = 56 - (24
               y = 32 pennies.

The number of pennies is 56-x or 56-24 or 32 pennies.

Checking:  24 nickles is $1.20 and 32 pennies is $0.32

            That's 56 coins.
            And indeed $1.20 + $0.32 = $1.52

Edwin