Their are 40 coin of dimes and quaters and they make $4.90 how much of each coin is their

1 dime = 10 cents
1 quarter = 25 cents

$4.90 = 490 cents

let q = quaters
let d = dimes 

d + q = 40  equation 1
10d + 25q = 490 equation 2

10d+ 10q = 400 equation 1 multiplied by 10
10d + 25q = 490 equation 2 multiplied by 1

-15q = -90
q = 90/15
q = 6

plug q into any one of the equations 

d + q = 40
d + 6 = 40
d = 40 - 6
d = 34

34 dimes and 6 quaters