Inez has 20 coins consisting of dimes and quarters. how many of each type does she have if all together she has $4.10

X = # dimes
y = # quarters

x+y = 20 so x = 20 - y
0.1x + 0.25y = 4.1

substitute x = 20 - y into 0.1x + 0.25y = 4.1

0.1x + 0.25y = 4.1
0.1(20 - y) + 0.25y = 4.1
2 - 0.1y + 0.25y = 4.1
0.15y = 2.1
 y = 2.1 / 0.15
 y = 14

x = 20 - 14 = 6

answer
Dimes: 6 coins
Quarters: 14 coins

Double check
6 + 14 = 20 coins total
6(0.1) + 14(0.25) = 0.6 + 3.5 = $4.10