Please show me how to solve:

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

answers for whole quiz

1. elimination
2. 2,1
3. substitution
4. 8,4
5. none
6. three lines
7. infinitely
8. $7.00
9. x=11 y=-5 z=-71
10. 4 five 10 one

1. Elimination

2. (2, 1)
3. Substitution
4. (8, 4)
5. None
6. III
7. Infinitely many solutions
8. $7.00
9. x = 11, y = -5, z = -71
10. 4 five-dollar bills, 10 one-dollar bills

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To solve this problem using elimination, we can set up a system of equations. Let's denote the number of one-dollar bills as "x" and the number of five-dollar bills as "y".

From the given information, we can write two equations:

Equation 1: The total number of bills is 14.
x + y = 14

Equation 2: The total value of the bills is $30.
1x + 5y = 30

To solve this system of equations by elimination, we will multiply Equation 1 by -1, so that when added to Equation 2, the "x" terms will cancel out. Here's how:

Multiply Equation 1 by -1:
-1(x + y) = -1(14)
-x - y = -14

Now, add this new equation to Equation 2:

(-x - y) + (1x + 5y) = -14 + 30

This simplifies to:
4y = 16

Now, divide both sides of the equation by 4 to solve for "y":

4y/4 = 16/4
y = 4

We have found that the number of five-dollar bills is 4.

To find the number of one-dollar bills, substitute the value of "y" into either Equation 1 or Equation 2. Let's use Equation 1:

x + 4 = 14

Now, subtract 4 from both sides of the equation:

x = 14 - 4
x = 10

Therefore, Sharon has 10 one-dollar bills and 4 five-dollar bills.

ONE*1+FIVE*5=30

where ONE is the number of ones, and FIVE is the number of fives.

ONE+FIVE=14
Five=14-ONE

ONE*1+(14-ONE)5=30
ONE+70-5*ONE=30
-4ONE=-40
ONE=8 bills, then FIVE =6