Casey has 21.40 in dimes and quarters, she has a total of 100 coins, how much of each kind of coin does casey have elimination method

A dime worth 10 cents. A quarter worth 25 cents. 
Let x be the number of cents and y be the number of quarters. 
then we get the equations:
10x+25y=2140
x+y=100.
multiply the second equation by -10 we get:
-10x-10y=-1000
Add this equation to the first equation we get:
15y=1140 then y=76 then x=100-76=24.
There were 24 dimes and 76 quarters.