1. Day 3: Ways That Two Lines Can Intersect
Unit 2: Linear Systems
Did you know that the average person falls asleep in 7 minutes?

2. Learning Goals
To be able to identify the different ways two lines can intersect

3. Your Teams A B C D E F Jeremy Stephanie Maddy Jacob Logan M Alex
Harrison
Chris
Michael
Kyle
Ali
Noah W
Claire
Maxx
Andrew
Sophia
Evan
Logan H
Ashmita
Adrian
Anusha
Eric
Stefanie
Colin
Carson
Kaitlyn
Noah H
Liz

4. To Do…
Graph both lines on the same grid by the method of your choice. Label each line clearly. Consider using different colours.
Team A
2𝑥+3𝑦=−4
−4𝑥−3𝑦=−1 B
3𝑥+2𝑦=6
6𝑥+4𝑦=5 C
𝑥−𝑦=5
3𝑥−3𝑦=15 D
3𝑥+2𝑦=8
6𝑥+4𝑦=40 E
𝑥+𝑦=2
2𝑥−3𝑦=9 F
𝑥−3𝑦=6
4𝑥=9𝑦+24

5. Team A
2𝑥+3𝑦=−4
−4𝑥−3𝑦=−1

6. Team B
3𝑥+2𝑦=6
6𝑥+4𝑦=5

7. Team C
𝑥−𝑦=5
3𝑥−3𝑦=15

8. Team D
3𝑥+2𝑦=8
6𝑥+4𝑦=40

9. Team E
𝑥+𝑦=2
2𝑥−3𝑦=9

10. Team F
𝑥−3𝑦=6
4𝑥=12𝑦+24

11. Questions to Answer How do the lines intersect? (How many times?)
Examine the two equations. Are there clues that tell you how the lines will intersect? Explain.
Can a linear system have exactly two solutions? Three solutions? Explain.

12. A Linear System Can Have…
No solution
One solution
Infinite solutions
Easily recognized when both are in 𝑦=𝑚𝑥+𝑏 form

13. No Solution Parallel lines Will never intersect
Slope is the same, y-intercept is different

14. One Solution
Have one intersection
Different slopes

15. Infinite Solutions Essentially the same line Intersect infinite times
One equation is a multiple of the other

16. Success Criteria
I CAN tell how two lines will interact by looking at the equation

17. To Do… pg. 59 #2a, 3abeg, 6 Extra help Tuesday after school (rm 209)
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Quiz tomorrow
AS Test Friday