1. 8.EE.8a Graphing Systems of Equations
Directions and Notes included on slides

2. Warm Up ( get all, work on all)
Solve the following equations for y
3x – 2y = 15
5y – x = 7
-3x – 4y = 10

3. Agenda Warm Up Sprint work: Graphing
Do It Yourself Partnerwork: Two Lines, One Graph
Mini Lesson: Graphing Systems of Linear Equations
Guided Practice
Practice Party
Debrief

4. Sprint work Graph as many linear equations as you can in 5minutes!
Two habaneros on tonight’s homework if you can handle the SPICY problems
5 minutes
Click the red circle to start the time.

5. Do It Yourself Partner Work
With your elbow partner, decide who will be Person A and Person B.
Person A – grab a piece of grid paper from the back
Person B- grab two different color markers from the bin
READ ALL THE DIRECTIONS ON THE HANDOUT!
10 minutes

6. DIY: Debrief
What did you notice about your lines after you graphed them?
What did they have that were the same? What made them different?
WHOLE GROUP DISCUSSION: 3 minute reflection on the graphing activity.

7. Mini Lesson Objective By the end of class today, we will be able to…
Describe what systems of equations are what the solution represents
Graph two linear equations the same Cartesian plane
Identify the point of intersection of the lines is the solution to both equations.

8. System of Equations Key Ideas
A system of equations is when you have two or more equations using the same variables.
The solution to the system is the point that satisfies ALL of the equations. This point will be an ordered pair.
When graphing, you will encounter three possibilities, but today we are going to focus on one: WHEN THE LINES INTERSECT
Popcorn call on students to read each key idea.

9. Think Aloud Find the solution to the system below. 𝑦=−𝑥−2 𝑦=4𝑥+3
Student’s know that during a think aloud. I am going to model how to solve this thinking through my approach step by step. If projected on a dry-erase board I model how to solve this problem while they take notes and watch (the lightbulb graphic is our in class signal for times when I just want them to watch me think through something)

10. Intersecting Lines
The point where the lines intersect is your solution.
The solution of this graph is (1, 2)
(1,2)

11. Find the solution of the system below
Think Aloud #2
Find the solution of the system below
2x + y = 4
x - y = 2
ONE WAY: Graph both equations but converting them to slope-intercept form.
2x + y = 4
y=-2x+4
y intercept = 4
slope = -2
x – y = 2
-y = -x +2
y = x - 2
y intercept = - 2
slope = 1
Students should be familiar with how to graph from standard form. But use this think aloud as another chance to model how they should think convert the problems when this arises.

12. Next Step: Graph the Two Equations
2x + y = 4
y = -2x +4
x - y = 2
y = x - 2
Where do the lines intersect?
(2, 0)
2x + y = 4
x – y = 2

13. Last Step: Check Your Answer
To check your answer, plug the point back into both equations.
2x + y = 4
2(2) + (0) = 4
x - y = 2
(2) – (0) = 2
Nice job…let’s try another!

14. Guided Practice Which of the following represents the solution to a
system of linear equations on graphs?
The slopes of the lines
The x-intercepts of the lines
The y-intercepts of the lines
The point at which the lines intersect
Have students show you with multiple choice cards or finger signals close to the chest of 1, 2, 3 or 4 so that you can get a pulse of who understands the key idea before revealing the answer.

15. Guided Practice
The system of equations represented by lines p and q is shown in the graph below. Based on the graph, what is the solution of the system of equations? A. (0, 0) C. (2, 1) B. (0, 3) D. (4, 2)
Same facilitaiton moves as on the slide above.

16. Guided Practice
What is a solution to both equations? y = x + 1 and y = -2x + 4
Have students talk you through how they would find do this step by step. Then do it on their own paper. Then reveal the answer.

17. First, solve each equation for "y =".
Guided Practice
2. Solve the following system graphically
4x – 6y = 12 and 2x + 2y = 6
First, solve each equation for "y =".
Students working on their own for a few minutes before we work through it as a group.

18. Next, graph the two lines
Guided Practice
2. Solve the following system graphically
4x – 6y = 12 and 2x + 2y = 6
Next, graph the two lines
Students working on their own for a few minutes before we work through it as a group.

19. Practice Party Complete the worksheet independent practice worksheet.
You may work with your critical friends group.

20. Key Ideas and Take-Aways for today’s lesson
Whole Class Debrief
Key Ideas and Take-Aways for today’s lesson
Use this time to call on students to share the key ideas from today’s lesson. They should be doing this from memory and without referencing the notes.