## Objective:

**To use linear combination to solve systems of linear equations.**

## Notes:

Steps to solve a system of equations by linear combination.- Think about the problem.
- Pick variables and write 'let' statements.
- Write two equations.
- Solve using a method from sections 7.1, 7.2, or 7.3.
- Write the answer in a complete sentence.

## Examples:

- Homer has a jar of nickels and quarters with a value of four dollars. There are 52 coins in all. How many nickels does Homer have? How many quarters does he have?

*Think about the problem.*

There are 52 coins (nickels and quarters). Each nickel is worth 5 cents and each quarter is worth 25 cents. The total value is $4 (400 cents).*Pick variables and write 'let' statements.*

Let n = the number of nickels

q = the number of quarters*Write two equations.*

n + q = 52 (The number of nickels plus the number of quarters is equal to 52.) 5n + 25q = 400 (The value of the nickels plus the value of the quarters is equal to 400 cents)

(Hint: Make sure to use the same units for all variables (pick either $ or ¢).*Solve.*

I chose to use the linear combination method (7.3) for this problem.*Write your answer as a complete sentence.*

Homer has 45 nickels and 7 quarters. (doh!)

- Lisa has a large rectangular bedroom. The length of her bedroom is five feet more than the width. The perimeter is 70 feet. What are the dimensions of her bedroom?

*Think about the problem.*

Perimeter is the distance around. (P = 2l + 2w)*Pick variables and write 'let' statements.*

Let l = the length of the bedroom

w = the width of the bedroom*Write two equations.*

l = w + 5 (The length is five feet more than the width.)

70 = 2l + 2w (Use the formula for perimeter of a rectangle.)*Solve.*

Since l is by itself already, I chose to use the substitution method (7.2) this time.*Write your answer as a complete sentence.*

Lisa's bedroom is 15ft by 20ft.