1. Linear Systems

2. What Do You Notice?

3. When will the two dots meet?
Questions
What do you notice?
What do you want to know?
When will the two dots meet?

4. What information would you like to have?
Where will the two dots meet?

5. How does this help us?

6. Calculating speed How do we calculate speed? Speed = ∆𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 ∆𝑡𝑖𝑚𝑒
The red dot moves cm/s = 3.1 cm/s
The blue dot moves cm/s = 5.9 cm/s

7. Creating equations
Create an equation for the position, d of each dot with respect to time, t
Red: 𝒅=𝟑.𝟏𝒕
Blue: 𝒅=𝟏𝟎𝟎−𝟓.𝟗𝒕

8. When will these two lines meet?
When will the distance and time be the same for both equations?
How could we find out?

9. Lets Check our answer!

10. Linear systems
A linear system is a set of linear equations (usually 2)
By solving a linear system we are looking for which values of the two variables satisfy all equations
We can solve a linear system by determining where the two lines meet (intersect) by graphing

11. example
Solve the following linear system by graphing: 6𝑥−3𝑦=−1 𝑦=−2𝑥+9