1 nickel = 5 cents

1 dime = 10 cents

Let

n = the number of nickels, n>=0, n is integer

d = the number of dimes, d>=0, d is integer

Sue has $2.35 = 235 cents in nickles and dimes:

5n + 10d = 235 divide both sides by 5

n + 2d = 47

She has 33 coins in all:

n + d = 33

We have the following system of equations:

n + 2d = 47

n + d = 33

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n = 19 nickles

d = 14 dimes

There are 19 nickles and 14 dimes.