Presentation on theme: "Unit 1 Modeling with Linear Equations Learning Goal: I can model real-life situations using linear equations."— Presentation transcript:
Unit 1 Modeling with Linear Equations Learning Goal: I can model real-life situations using linear equations
Warm-Up: Graph of the Day What are the y-intercepts for the yellow cab and the blue cab? What do these values represent. You miss the bus and need to take a cab 5km to school; which cab should you choose? If you wanted to travel as far as possible with $6, which cab should you choose?
Linear Systems Many real-life situations can be modeled using linear equations. When 2 or more equations are used, it is called a system of equations. If all of the equations are linear, its called a linear system.
Linear Systems The solution to a linear system is an ordered pair that satisfies all equations Graphically, the solution is the point where two lines intersect
Modeling with Linear Equations At the zoo gift shop, posters of polar bears are $1 and poster of penguins are $6. Charles spent $32 to buy 7 posters, how many of each did he buy? Let x represent the number of polar bear posters Let y represent the number of penguin posters
Modeling with Linear Equations Jamie went out to her grandfather's farm. Her grandfather has pigs and chickens on his farm. She noticed that there were a total of 26 heads and 68 feet among them. How many chickens and how many pigs did her grandfather have?
Modeling with Linear Equations Yasmin has $8000 to invest and would like to earn $500 from the money. How much should she invest in a stock that has been paying 10% annual return and how much should she invest in savings bonds that pay 4% annual interest?
Modeling with Linear Systems José travelled 95km from Oakville to Oshawa by car and GO train. The car averaged 60km/h, and the train averaged 90km/h. The whole trip took 1.5h. How long was he in the car? In the train?
Homework Pg # 7, 10, 19, 23, 26 Just define variables and write 2 equations; you dont need to solve.