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


                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
nickels        x      $0.05      $0.05x
pennies        y      $0.01      $0.01y
-------------------------------------------
TOTALS       175      -----      $4.75

 The first equation comes from the second column.

  

                 x + y = 175

 The second equation comes from the last column.
  

           0.05x + 0.01y = 4.75

Get rid of decimals by multiplying every term by 100:

                 5x + 1y = 475

 So we have the system of equations:
           .

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

            x + y = 175
                y = 175 - x

Substitute (175 - x) for y in 5x + 1y = 475

  5x + 1(175 - x) = 475
    5x + 175 - 1x = 475
         4x + 175 = 475
               4x = 300
                x = 75 = the number of nickels.

Substitute in y = 175 - x
              y = 175 - (75)
              y = 100 pennies.

Checking:  75 nickels is $3.75 and 100 pennies is $1.00
            That's 175 coins.
            And indeed $3.75 + $1.00 = $4.75
Edwin