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

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

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

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

Team A 2𝑥+3𝑦=−4 −4𝑥−3𝑦=−1

Team B 3𝑥+2𝑦=6 6𝑥+4𝑦=5

Team C 𝑥−𝑦=5 3𝑥−3𝑦=15

Team D 3𝑥+2𝑦=8 6𝑥+4𝑦=40

Team E 𝑥+𝑦=2 2𝑥−3𝑦=9

Team F 𝑥−3𝑦=6 4𝑥=12𝑦+24

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.

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

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

One Solution Have one intersection Different slopes

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

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

To Do… pg. 59 #2a, 3abeg, 6 Extra help Tuesday after school (rm 209) Check the website daily for updates, missed notes, assignment solutions www.mrsmccrum.weebly.com Quiz tomorrow AS Test Friday