copyright © 2010 pearson education, inc. all rights reserved sec 5.1 - 1 4.1 systems of linear...
TRANSCRIPT
![Page 1: Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 5.1 - 1 4.1 Systems of Linear Equations In Two Variables](https://reader034.vdocuments.site/reader034/viewer/2022051516/56649e185503460f94b0470d/html5/thumbnails/1.jpg)
Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 5.1 - 1
4.1
Systems of Linear Equations
In Two Variables
![Page 2: Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 5.1 - 1 4.1 Systems of Linear Equations In Two Variables](https://reader034.vdocuments.site/reader034/viewer/2022051516/56649e185503460f94b0470d/html5/thumbnails/2.jpg)
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.1 - 2
4.1 Systems of Linear Equations in Two Variables
Systems of Equations
Suppose we wished to cut a 10-foot length of conduit into two pieces such that one piece is 4 feet longer than the other. We are looking for two numbers whose sum is 10 and whose difference is 4. If we let x represent the larger of the two numbers and y the other number, we immediately get two equations.
We call such an arrangement a system of two equations in two variables.
![Page 3: Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 5.1 - 1 4.1 Systems of Linear Equations In Two Variables](https://reader034.vdocuments.site/reader034/viewer/2022051516/56649e185503460f94b0470d/html5/thumbnails/3.jpg)
Sec 5.1 - 3
4.1 Systems of Linear Equations in Two Variables
Solution of a Systems of Equations
Given the following system of equations, determine whether the given ordered pair is a solution of the system.
The ordered pair must be a solution of both equations to be a solution.
![Page 4: Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 5.1 - 1 4.1 Systems of Linear Equations In Two Variables](https://reader034.vdocuments.site/reader034/viewer/2022051516/56649e185503460f94b0470d/html5/thumbnails/4.jpg)
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.1 - 4
4.1 Systems of Linear Equations in Two Variables
Deciding Whether an ordered Pair is a Solution
Given the following system of equations, determine whether the given ordered pair is a solution of the system.
![Page 5: Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 5.1 - 1 4.1 Systems of Linear Equations In Two Variables](https://reader034.vdocuments.site/reader034/viewer/2022051516/56649e185503460f94b0470d/html5/thumbnails/5.jpg)
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.1 - 5
4.1 Systems of Linear Equations in Two Variables
Possible Solutions for a Linear System of Two Variables
![Page 6: Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 5.1 - 1 4.1 Systems of Linear Equations In Two Variables](https://reader034.vdocuments.site/reader034/viewer/2022051516/56649e185503460f94b0470d/html5/thumbnails/6.jpg)
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.1 - 6
4.1 Systems of Linear Equations in Two Variables
The Substitution Method for Solving Systems
![Page 7: Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 5.1 - 1 4.1 Systems of Linear Equations In Two Variables](https://reader034.vdocuments.site/reader034/viewer/2022051516/56649e185503460f94b0470d/html5/thumbnails/7.jpg)
4.1 Systems of Linear Equations in Two Variables
Solving a System by Substitution
![Page 8: Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 5.1 - 1 4.1 Systems of Linear Equations In Two Variables](https://reader034.vdocuments.site/reader034/viewer/2022051516/56649e185503460f94b0470d/html5/thumbnails/8.jpg)
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.1 - 8
4.1 Systems of Linear Equations in Two Variables
The Elimination Method for Solving Systems
![Page 9: Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 5.1 - 1 4.1 Systems of Linear Equations In Two Variables](https://reader034.vdocuments.site/reader034/viewer/2022051516/56649e185503460f94b0470d/html5/thumbnails/9.jpg)
4.1 Systems of Linear Equations in Two Variables
Solving a System by Elimination
![Page 10: Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 5.1 - 1 4.1 Systems of Linear Equations In Two Variables](https://reader034.vdocuments.site/reader034/viewer/2022051516/56649e185503460f94b0470d/html5/thumbnails/10.jpg)
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.1 - 10
4.1 Systems of Linear Equations in Two Variables
Solving a System with Fractional Coefficients
![Page 11: Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 5.1 - 1 4.1 Systems of Linear Equations In Two Variables](https://reader034.vdocuments.site/reader034/viewer/2022051516/56649e185503460f94b0470d/html5/thumbnails/11.jpg)
4.1 Systems of Linear Equations in Two Variables
Some Special Systems
Some systems of linear equations have no solution or an infinite number of solutions.
![Page 12: Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 5.1 - 1 4.1 Systems of Linear Equations In Two Variables](https://reader034.vdocuments.site/reader034/viewer/2022051516/56649e185503460f94b0470d/html5/thumbnails/12.jpg)
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.1 - 12
4.1 Systems of Linear Equations in Two Variables
Some Special Systems
![Page 13: Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 5.1 - 1 4.1 Systems of Linear Equations In Two Variables](https://reader034.vdocuments.site/reader034/viewer/2022051516/56649e185503460f94b0470d/html5/thumbnails/13.jpg)
4.1 Systems of Linear Equations in Two Variables
Some Special Systems
![Page 14: Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 5.1 - 1 4.1 Systems of Linear Equations In Two Variables](https://reader034.vdocuments.site/reader034/viewer/2022051516/56649e185503460f94b0470d/html5/thumbnails/14.jpg)
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 5.1 - 14
4.1 Systems of Linear Equations in Two Variables
Some Special Systems