5.6 Notes, Date _________________

Creating Equations

Entry Ticket ReviewWhat are the variables? c = coffee, d = donuts

What equations can we create? c + d = 100, 3c + d = 180

What is the solution? 40 coffees and 60 donuts

How would this look on a graph? The 2 lines would intersect at the point (40,60)

Note: To solve a system with n variables, you need at least n equations! Mr. Patterson is thinking of 5 numbers. How many

equations would we need to solve this system? Explain.We would need at least 5 equations because there are 5 numbers we are trying to find.

Example: Claire babysits and works at Market Basket. She worked a total of 20 hours this week and made $170. She gets $10 per hour for babysitting and $8 per hour at Market Basket.

Step 1 – Identify and Define the variables

Babysitting = b, Market Basket = m

Step 2 – Write Equations

b + m = 2010b + 8m = 170

Steps in Creating Systems

Example 1You are trying to choose between 2 cell phone plans. Plan A charges a $20 set up fee, and 5 cents per minute. Plan B does not charge a set up fee, but they charge 15 cents per minute.

1. Define the variables. p = price of plan, m = minutes

2. Write an equation for Plan A and an equation for Plan B.

Plan A: p = .05m + 20 Plan B: p = .15m

3. Solve the system using substitution.

p = .05m + 20p = .15m

.15m = .05m + 20

.10m = 20

m = 200

p = .15(200)

p = 30

Solution: (200, 30)

4. What does the solution mean? Both plans cost $30 when you use 200 minutes

The students in Mr. Smith’s class want to know how old he is. He tells them that the combined age of he and his brother is 63 years and that he is 3 years older than his brother.

1. Define the variables. s = Mr. Smith’s age, b = his brother’s age

2. Write a system of equations for this scenario.

s + b = 63 s = b +3

3. Which method would be the easiest way to solve this system?

s + b = 63s = b + 3

b + 3 + b = 63

2b + 3 = 63

b = 30

s = 30 + 3s = 33

Solution: (30, 33)

4. How old is Mr. Smith?

Example 2

Substitution

2b = 60

33 years old