Sammi has $21.40 in dimes and quarters, with a total of 100 coins. how many of each type of coin does she have?

X= dimes
y= quarters

QUANTITY EQUATION:
x+y=100

COST EQUATION:
$0.10x+$0.25y=$21.40

STEP 1:
Solve for one variable in quantity equation.

x+y=100
subtract y from both sides
x= 100-y

STEP 2:
Substitute answer above in cost equation.

Dimes= $0.10
Quarters= $0.25

(Value of dime * dime quantity) + (value of quarter * quarter quantity)= total value

$0.10x+$0.25y=$21.40
0.10(100-y) + 0.25y=21.40

multiply 0.10 by all in parentheses
(0.10*100)+(0.10*-y) + 0.25y= 21.40

10 - 0.10y + 0.25y= 21.40
10 + 0.15y= 11.40

subtract 10 from both sides
0.15y= 11.40

divide both sides by 0.15
y= 76 number of quarters

STEP 3:
substitute y=76 in either equation.

x+y=100
x+76=100

subtract 76 from both sides
x= 24 number of dimes

Hope this helps! :)