Upcoming SlideShare
×

# Lecture 6.1 6.2 bt

417 views

Published on

Published in: Technology
0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
Your message goes here
• Be the first to comment

• Be the first to like this

Views
Total views
417
On SlideShare
0
From Embeds
0
Number of Embeds
7
Actions
Shares
0
4
0
Likes
0
Embeds 0
No embeds

No notes for slide

### Lecture 6.1 6.2 bt

1. 1. Today’s Agenda  Attendance / Announcements  Collect Projects  Return Exams  Sections 6.1, 6.2  Quiz Friday
2. 2. Exam Schedule  Exam 4 (Ch 6,7) Fri 11/15  Exam 5 (Ch 10) Thur 12/5  Final Exam (All) Thur 12/12
3. 3. Review: Graphing/Equations of Lines Sections 2.1, 2.2
4. 4. Systems of Linear Equations 3x y 9 2x y 1 A solution of a system of linear equations is an ordered pair that satisfies both equations.
5. 5. Solve by Graphing 3x y 9 2x y 1 So, the solution of the system is (2, -3)
6. 6. Solve by Graphing 2x 4 y 8 y 1 2 x 2 So, the solution of the system is ?
7. 7. Solve by Graphing x 2y 2x 4 y 3 6 So, the solution of the system is ?
8. 8. Solve by Graphing
9. 9. Solving Systems Algebraically The Substitution Method • Works well when it is easy to solve for one of the variables • Substitute expression into other equation, Solve. • Plug solved value back into either equation to find solution. • Check the solution in both equations
10. 10. The Substitution Method 3x y 6 6x 5 y 23 • What does this tell us about the graphs of the system?
11. 11. The Substitution Method 3x y 9 2 y 6x 7 • What does this tell us about the graphs of the system?
12. 12. The Substitution Method 4x y 8x 2 y 2 4 • What does this tell us about the graphs of the system?
13. 13. The Substitution Method x 2y 2x y 3 5 • What does this tell us about the graphs of the system?
14. 14. Solving Systems Algebraically The Elimination Method • We can multiply/divide any linear equation. • We can also add/subtract linear equations together. • Use algebra to eliminate one of the variables, solve for the other. • Check the solution in both equations
15. 15. The Elimination Method 5x y 4 3x 2 y 1 Addition Method - Want to get “opposite coefficients” - Then add equations to eliminate variable Subtraction Method - Want to get “same coefficients” - Then subtract equations to eliminate variable
16. 16. The Elimination Method 2x 3y 2 2 y 3 x 12 Want to rewrite to line up like terms
17. 17. The Elimination Method 2 x 5 y 14 7x 6 y 2
18. 18. Applications The sum of two numbers is 70 and their difference is 24. Find the two numbers.
19. 19. Solving Larger Systems using Substitution • Use algebra to isolate one of the variables, substitute into the other two. • Solve the two variable system, use Substitution find the first variable • Check solution in all three equations
20. 20. The Substitution Method 2x y z 2 x 3 y 2z 1 x y z 2
21. 21. The Substitution Method 2x 3 y 2 x y 4z 16 3x 2 y z 7
22. 22. The Substitution Method x 2y z 5 2x y z 2x 4 y 2z 2 2
23. 23. Classwork / Homework • Page 317 •1 – 15 odd, 19 • Page 329 •9, 39, 41, 45