suppose Tom has d dimes and q quarters.
total number of coins: d+q=23
total amount of money: 10d+25q=425
multiply the first equation by 10: 10d+10q=230
subtract the new equation from the second equation: 25q-10q=425-230,
15q=195
q=13
d=23-13=10
Tom has 10 dimes and 13 quarters.