Lesson 8.8 Systems of Linear Equations Essential Question: How do you solve a system of linear equations by graphing?

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Presentation transcript:

Lesson 8.8 Systems of Linear Equations Essential Question: How do you solve a system of linear equations by graphing?

Before we start… Is there a point of intersection? Where?

What is a system of linear equations? A linear system consists of two or more linear equations in the same variables.

What is a solution of a linear system? An ordered pair (x, y) that is a solution of each equation in the system Solutions correspond to points where the graphs of the equations in a system intersect.

What is the solution here?

City Populations The graph shows the estimated populations of the Buffalo, New York area and the Charlotte, North Carolina area. Use the graph to find the year in which the populations of these two areas were the same. What was the population?

How many solutions can a linear system have? One solution No solution Infinitely many solutions

How do you solve a system by graphing?

Juice You bought 15 one-gallon bottles of apple juice and orange juice for a school dance. The apple juice was on sale for $1.50 per gallon bottle. The orange juice was $2 per gallon bottle. You spent $26. Write algebraic models for the situation. Then graph the algebraic models. How many bottles of each type of juice did you buy?

Internet Service A company offers two plans for high-speed Internet service. With Plan A, you pay $200 for the modem and $30 per month for service. With Plan B, the modem is free and you pay $40 per month for service. a.After how many months are the total costs of the plans the same? b.When is Plan A a better deal? What is Plan B a better deal?

Money Kate has $600 in her bank account and she deposits an additional $30 into the account each week. Jim has $440 in his bank account and he deposits an additional $50 into the account each week. a.After how many weeks will Jim and Kate have the same amount in their accounts? b.When does Kate have more money in her account than Jim has? When does Jim have more money than Kate?

How do you solve a system of linear equations by graphing?

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