1. Monday November 3- Wednesday November 5
Section 3.1
Monday November 3- Wednesday November 5

2. Section 3.1 Solving Systems Using Tables and Graph Engage
For the following two problems, graph both functions either using their equations provided and find the point of intersection.
𝑦=−𝑥 𝑦=𝑥−2
𝑦= 3 2 𝑥− 𝑦=−2𝑥+7

3. What is a system of equations?
A set of two or more equations, which have two or more related unknown variables is called a system of equations.
A linear system consists of linear equations.
A solution is a set of values for the variables that makes all the equations true

4. Explore: Graphing Calculators
Using the graphing calculators and the instructions given, find the solutions of the systems of equations represented by the following tables.
You will use the calculator to graph the scatter plot, find the linear regressions of both lines, and find the point of intersection.
Write the linear regression (y=ax+b) for both equations you find in each question.
Check the solution with both equations in the system.
Hint: Let x be the number of years since Model your y-value as follows: 12,911,994 = 12.9 million

5. How did we do?
What is the linear regression of the data for New York City? What is the linear regression of the data for Los Angeles?
What is the point of intersection of the two sets of data?

6. Evaluation: Look Back
Create a chart like the one below on your own sheet of paper. Think about what you learned today and how you learned it. There should be at least two sentences in each box.
What I learned
How I learned it

7. Engage: Observations and Prediction
Each time you have solved a linear system of equations that has had an intersection, how many solutions were you able to find? What would happen if two lines were parallel? How many solutions would there be?

8. Exploring Classifications of Linear Systems of Equations
Using a large sheet of graph paper and two different color popsicle sticks, complete the Classifications of Linear Systems of Equations worksheet. Answer each of the questions below on your own sheet of paper.
Your two popsicle sticks represents a system of equations. Place the popsicle sticks in such a way that they are intersecting. How many points of intersection are there?
How many solutions are there for this system of equations?
Place the popsicle sticks stacked one on top of the other. How many points of intersection are there?
Place the popsicle sticks parallel to one another. How many points of intersection are there?

9. Explanation: Classification of Systems of Equations
You can classify a system of two linear equations by the number of solutions. A system can have zero, one, or infinitely many solutions.
The graphs of parallel lines do not intersect, so there are no solutions.
If two equations represent the same line, there are infinitely many solutions.

10. Example
Does this system have zero, one, or infinitely many solutions? What is the classification of this system of equations?
−3𝑥+𝑦=4
𝑥− 1 3 𝑦=1

11. You Do
Does this system have zero, one, or infinitely many solutions? What is the classification of this system of equations?
7𝑥−𝑦=6
−7𝑥+𝑦=−6

12. Example: Classifying Systems without Graphing
Without graphing, how can we classify a system of equations?
Make sure both equations are in slope intercept form. If they have the same slope, they are either parallel or coinciding.
Coinciding systems will have the same slope and y-intercept. Parallel lines will have the same slope but different y-intercepts.
What is the classification of this system of equations?
4𝑦−2𝑥=6
8𝑦=4𝑥−12

13. You Do: Classifying Systems without Graphing
What is the classification of this system of equations?
2𝑥+3𝑦=1
4𝑥+𝑦=−3

14. Elaborate: Let’s Practice
Open your text books to pg. 151 #20-24
Practice classifying the systems of equations. Whatever you do not have complete will be for homework.

15. ROPES #8: Warm Up
After trick-or-treating John has an original amount of candy represented by the variable c. If Mallory eats 12% of Zachary's candy every day, what is the function rule to represent the amount of candy left after the 4th day?
How much candy is left after the 4th day if Zachary started out with 350 pieces of candy ?

16. ROPES #8
After trick-or-treating Zachary has an original amount of candy represented by the variable c. If Addison eats 15% of Zachary's candy every day, what is the function rule to represent the amount of candy left after the 3rd day?
How much candy is left after the 3rd day if Zachary started out with 400 pieces of candy ?

17. Evaluate: Create the Problem
Create a system of equations for each of the three classifications of linear systems of equations.
Support your answer with reasoning for your choice of systems of equations.
1) Intersecting lines 2) Coinciding lines 3) Parallel Lines