Standard: ee.8a: Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

Day 1 & 2 established what a point of intersection looks like on a graph (begin with it again to reiterate). Day 3 & 4 need to begin to focus on that these points of intersection “satisfy both equations simultaneously”.

*Focus question*: What does the solution to a system of two linear equations graphically and mathematically look like?

*Bellwork*: What did changing the headstart distance of “Half-Speed Julio” do to his linear graph? Can you make a quick sketch to illustrate what you are talking about?

*Recap Yesterday: *At what time and distance would “Half-Speed Julio” and Rich be at the same place?

[in notes] Give a possible “solution” (there are infinite) to the equation y=2x+3. (hint: your answer will be in the form of an ordered pair)

[referencing homework problem] how many solutions do these two graphs have in common? Can you prove that the solution works for both graphs mathematically?

http://map.mathshell.org/download.php?fileid=1154

- Accurate Method vs. Estimation Method
- “Can you write an equation for each?”
- Graph it using Desmos.com
- “Is the estimation method close enough that it is worth using?”
- “Mathematically, why do the two equations give you close answers?”
- “Will the two equations ever give you the same answer?” “How do you know?”s
- “When do they actually give you the same answer?” Use the graph to prove it. Use math to prove it.

*Homework: *Finish questions 4 and 5.

**Day 3 Reflection:**

The majority of class was spent on understanding what a solution is and how many solutions a linear equation can have (infinite) vs. most systems of equations (one). I will spend a separate day to teach infinite solutions and no solutions. Students then began the converting Celsius to Fahrenheit activity above, but we only reached graphing the two equations in Desmos. Students had to finish 4 and 5 on their own.

## So, what do you think ?