Answer: She has 13 dimes and 37 nickels.
Explanation:
We know that
1 dollar = 100 cents
Then, the value of one dime =10 cents =$0.1
and the value of one nickel = 5 cents = $0.05
Given : Elizabeth has 50 coins in nickels and dimes only and has a total of $3.15.
Let x be the number of dimes and y be the number of nickels , then the required system of equation would be :-

Multiply 10 to eqn (2), we get

Subtract eqn (3) from eqn (1), we get

Divide both sides by 0.15, we get

Put value of y in (1), we get

Therefore, she has 13 dimes and 37 nickels.