let

x = the number of dimes, x is positive integer

y = the number of nickles, y is positive integer

1 dime = 10 cents

1 nickle = 5 cents

she has 33 coins in all

x + y = 33

Ayana has $2.35 in nickels and dimes that is 235 cents

10x + 5y = 235 divide both sides by 5

2x + y = 47

by solving the system of equations

x + y = 33

2x + y = 47

we get

x = 14 dimes

y = 19 nickles

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Ayana has 14 dimes and 19 nickles.