1. Graphing Substitution Elimination
Systems of Equations
Graphing
Substitution
Elimination

2. Model
Emily is moving to a new apartment and wants to rent a 10-foot truck. She calls both U-Haul and Bob’s truck rental to compare prices. U-Haul is $19.95 per day and $0.79 per mile. Bob’s is $24.95 per day and $0.75 per mile.
Write equations for two companies total rental quotes for one day.
Graph on same coordinate plane
Determine the distance when both companies will cost the same.

3. Practice
A company wants to print flyers for advertising a new product. There are two options to produce the flyers.
Traditional printing cost is $250 for setup and $0.15 per page printed
Digital Printing charge $50 for setup and $0.20 per page printed.
Determine the equations
Graph on the same coordinate plane
Determine when both printing options will cost the same.

4. Sketch
Given two equations sketch the lines on the same coordinate plane.
𝑦= 2 3 𝑥 −7
𝑦=−𝑥+3

5. Sketch: 𝑦= 1 4 𝑥−2 𝑦=− 1 3 𝑥+5

6. Application a) Write a model for geothermal energy
Year
Geothermal
Wind
2003
5.37
1.79
2004
5.43
2.24
2005
5.28
2.8
2007
5.12
4.69
a) Write a model for geothermal energy
b) Write a model for wind energy
c) Determine when both are the same.

7. Graphing Calculator
𝑦=2𝑥+7 𝑦=5𝑥 −3.5 After putting into stat plot determine the solution.

8. Types of Systems
Consistent
Inconsistent

9. Determine the type of system
𝑦=3𝑥+5 𝑦=3𝑥 −2 𝑦= 2 5 𝑥−10 𝑦=0.2𝑥+1 𝑦= 1 2 𝑥+6 2𝑥 −4𝑦=−24

10. Algebraic Method
Solving systems by substitution.
𝑤=5𝑘+7
𝑤=−3𝑘+23

11. Determine the solution by substitution
𝑦=4𝑥 −5 𝑦=𝑥+22

13. Application
Using the model from Chapter 2.1 for geothermal and wind energy, find the year when the amount of geothermal and wind energy produced will be the same.
𝐺 𝑡 =−0.08𝑡+5.68
𝑊 𝑡 =0.82𝑡 −1.03
Where G(t) is the percentage of renewable energy produced by using geothermal energy t years since 2000 and W(t) is the percentage of renewable energy produced by using wind energy t years since 2000.

14. a) Find the equations b) Find when the sales will result in the same monthly salary for both options.
As a new sales employee, you are given two salary structures to choose from. The first option has a base salary of $1200 per month and 7% commission on sales made. The second option has a base salary of $800 per month and 9% on sales commission made.

15. Elimination Solving systems by canceling one of the variables. 7𝑥+3𝑦=6
4𝑥 −6𝑦=42

16. Solve
4𝑎+9𝑏=2 12𝑎+6𝑏=48

17. Mixing Solutions
Yolanda needs 70ml of 45% saline sln for a science experiment. She has some 60% saline sln and some 20% saline sln. How much of each of these slns should Yolanda combine to get the 70ml of 45% saline sln she needs?