# Unit 1 Modeling with Linear Equations

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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, it’s 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 You were probably introduced to these kinds of problems in elementary school; they may have been called ‘guess and check’ problems or ‘trial and error’ problems. These problems can be represented with linear systems During this unit, we will learn a more prescribed method for solving these problems (more accurate than guess and check). One of the most challenging aspects is constructing the equations based on a written description. Today we are going to practice constructing linear systems and not worry about solving the problem just yet. In these problems, there are usually 2 types of information (in this case # and cost). We need one equation for each type of info. Start by defining variables (use the question ‘how many’ as a guide) and use variable to come up with 2 equations (one for number and one for cost).

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? What are the 2 pieces of information? Define variables Use variables to make one equation for each type of information

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? What are the 2 pieces of information? Define variables Use variables to make one equation for each type of information

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? What are the 2 pieces of information? Define variables Use variables to make one equation for each type of information

Homework Pg # 7, 10, 19, 23, 26 Just define variables and write 2 equations; you don’t need to solve.