Sharon has some one dollar bills and som five dollar bills. She has 14 bills. The value of the bills are $30. Solve a system of equations using elimination to find how many of each kind of bill she has

Let the no. of one dollar bills be x and the no. of five dollar bills be y.

She has 14 bills = > 1st equation = > x+y=14

The value of the bills are $30 = > 2st equation = > ($1) x + ($5) y = 30

Simultaneous equations:

x + y = 14 = > x = 14 - y

x + 5y = 30

Sub x = 14 - y into x + 5y = 30,

ie. (14 - y) + 5y = 30 = > 14 + 4y = 30 = > 4y = 16 = > y=4

Lets x = # of one dollar bills, y = # of five dollars bills

x + y = 14 so x = 14-y

x + 5y = 30

substitute x = 14-y into x + 5y = 30

x + 5y = 30

14 - y + 5y = 30

4y = 16

y = 4

x = 14 - y = 14-4=10

# of one dollars bills = 10 ($1x10 = $10)

# of five dollars bills = 4 ($5 x 4 = 20)

double check

$10+$20 = $30 (The value of the bills are $30)

4+10=14 (She has 14 bills)