1. 6.2 Solving Systems by Substitution
Objectives:
Solve systems of linear equations in two variables by substitution.

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

3. 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.

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

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

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?

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

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

9. 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

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

11. Practice:
Practice 6.2 WS

12. Homework
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