6.2 Solving Systems by Substitution Objectives: Solve systems of linear equations in two variables by substitution.

Example 1: Solve 𝑦=3𝑥−1 for x when – A. 𝑦=11 B. 𝑦=𝑥 C. 𝑦=−10 D. 𝑦=2𝑥+7

Why is graphing not always the most useful way to solve a system of equations? We don’t always land on whole numbers! Remember – when solving a system of linear equations we are looking for an ordered pair that makes both equations true. We will use substitution when: Both equations are solved for 1 variable. 1 equation is solved for a variable, and one is in standard form.

Example 2: Solve each system by substitution. A. 𝑦=3𝑥 𝑦=𝑥−2 B. 𝑥=3𝑦+1 𝑥=𝑦−7

Example 2: continued... C. 𝑦+2𝑥=−4 𝑥=−𝑦−7 D. 𝑦=𝑥+1 4𝑥+𝑦=6

Example 3: Josie is deciding between two cell phone plans Example 3: Josie is deciding between two cell phone plans. The first plan has a $50 sign-up fee and costs $20 a month. The second plan has a $30 sign-up fee and costs $25 a month. After how many months will the total cost be the same? What will the cost be? If Josie has to sign up for a one year contract, which plan would be cheaper?

If both equations are in standard form: You must solve one of them for a variable and then substitute.

Example 4: Solve each system by substitution. A. 𝑥+2𝑦=−1 𝑥−𝑦=5 B. 2𝑥+𝑦=−6 −5𝑥+𝑦=1

Trivia 1. Which TV show has the characters:Rachel, Ross, Monica, Joey, Chandler, and Phoebe? Friends 2. Which Disney movie has the characters: Prince Eric, Sebastian, Flounder, Ursula, and King Triton? Little Mermaid

Example 4: Solve each system by substitution. C. 2𝑥−𝑦=8 𝑦−2𝑥=−3 D. 4𝑥−3𝑦=1 6𝑦−8𝑥=−2

Practice: Practice 6.2 WS

Homework Page 347: 9-23 odd