To view this presentation, you'll need to enable Flash.

Show me how

After you enable Flash, refresh this webpage and the presentation should play.

Loading...

PPT – SYSTEMS OF LINEAR EQUATIONS: PowerPoint presentation | free to download - id: 36747-MjdhO

The Adobe Flash plugin is needed to view this content

View by Category

Presentations

Products
Sold on our sister site CrystalGraphics.com

About This Presentation

Write a Comment

User Comments (0)

Transcript and Presenter's Notes

SECTION 6.1

- SYSTEMS OF LINEAR EQUATIONS
- SUBSTITUTION AND ELIMINATION

MOVIE THEATER TICKET SALES

SEE EXAMPLE 1 SEE EXAMPLE 2

EQUIVALENT SYSTEMS OF EQUATIONS

Linear System More than one linear equation

considered at a time. Solution - ordered pair (or

triple) that satisfies both (or all) equations

simultaneously.

CONSISTENT VS. INCONSISTENT

When a system of equations has at least one

solution, it is said to be consistent otherwise,

it is called inconsistent.

THREE POSSIBILITIES FOR A LINEAR SYSTEM

x - y 1 x - y 3

x - y 1 2x - y 4

x - y 1 2x - 2y 2

No Solution

One Solution

Infinitely Many Solutions

SOLVING A SYSTEM BY SUBSTITUTION

2x y 5 - 4x 6y 12

RULES FOR OBTAINING AN EQUIVALENT SYSTEM

1. Interchange any two equations. 2. Multiply (or

divide) each side of an equation by a nonzero

constant. 3. Replace any equation in the system

by the sum (or difference) of that equation and

a nonzero multiple of any other equation in the

system.

SOLVING A SYSTEM BY ELIMINATION

- 2x 3y 1
- x y - 3
- Multiply equation 2 by 2
- Replace equation 2 with the sum of equations 1

and 2.

MOVIE THEATER TICKET SALES

DO EXAMPLE 5

AN INCONSISTENT SYSTEM

2x y 5 4x 2y 8

AN DEPENDENT SYSTEM

2x y 4 - 6x - 3y - 12

3 EQUATIONS, 3 UNKNOWNS

2 x 4y - 2 z - 10 - 3x 4y - 2 z 5 5x

6y 3 z 3

x 2 y - z - 5 - 3x 4y - 2 z

5 5x 6y 3 z 3

Dividing 1st equation by 2 to make leading

coefficient equal to 1.

EXAMPLE

x 2 y - z - 5 - 3x 4y - 2 z 5

3x 6 y - 3 z - 15 - 3x 4y 2z 5

10y 5z -10

Mult. 1st eqn by 3 and add to 2nd

EXAMPLE

x 2 y - z - 5 5x 6y 3 z 3

-5x - 10 y 5 z 25 5x 6y 3z 3

- 4y 8z 28

Mult. 1st eqn by -5 and add to 3rd

EXAMPLE

Now we have 2 equations in only y z 10y -

5 z -10 - 4y 8 z 28

Divide 1st equation by 5 Divide 2nd equation by 4

EXAMPLE

2y - z - 2 - y 2 z 7

2y z -2 -2y 4z 14

3z 12 z 4

Multiply 2nd equation by 2 add to 1st

EXAMPLE

2y z -2 2y 4 -2 2y 2 y 1

x 2y z - 5 x 2 (1) - 4 - 5 x - 2 -

5 x - 3

(-3, 1, 4)

EXAMPLE

DO EXAMPLES 9, 10, 11

- CONCLUSION OF
- SECTION 6.1

About PowerShow.com

PowerShow.com is a leading presentation/slideshow sharing website. Whether your application is business, how-to, education, medicine, school, church, sales, marketing, online training or just for fun, PowerShow.com is a great resource. And, best of all, most of its cool features are free and easy to use.

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

Recommended

«

/ »

Page of

«

/ »

Promoted Presentations

Related Presentations

Page of

Home About Us Terms and Conditions Privacy Policy Presentation Removal Request Contact Us Send Us Feedback

Copyright 2018 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

Copyright 2018 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

The PowerPoint PPT presentation: "SYSTEMS OF LINEAR EQUATIONS:" is the property of its rightful owner.

Do you have PowerPoint slides to share? If so, share your PPT presentation slides online with PowerShow.com. It's FREE!