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.