CHAPTER 5 5-1 Solving Systems by Graphing. Objectives Identify solutions of linear equations in two...
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Transcript of CHAPTER 5 5-1 Solving Systems by Graphing. Objectives Identify solutions of linear equations in two...
![Page 1: CHAPTER 5 5-1 Solving Systems by Graphing. Objectives Identify solutions of linear equations in two variables. Solve systems of linear equations in two.](https://reader036.fdocuments.us/reader036/viewer/2022082816/56649ceb5503460f949b6eaa/html5/thumbnails/1.jpg)
CHAPTER 5 5-1 Solving Systems by Graphing
![Page 2: CHAPTER 5 5-1 Solving Systems by Graphing. Objectives Identify solutions of linear equations in two variables. Solve systems of linear equations in two.](https://reader036.fdocuments.us/reader036/viewer/2022082816/56649ceb5503460f949b6eaa/html5/thumbnails/2.jpg)
Objectives • Identify solutions of linear equations in two
variables. •Solve systems of linear equations in two
variables by graphing.
![Page 3: CHAPTER 5 5-1 Solving Systems by Graphing. Objectives Identify solutions of linear equations in two variables. Solve systems of linear equations in two.](https://reader036.fdocuments.us/reader036/viewer/2022082816/56649ceb5503460f949b6eaa/html5/thumbnails/3.jpg)
System of linear equations
•A system of linear equations is a set of two or more linear equations containing two or more variables. A solution of a system of linear equations with two variables is an ordered pair that satisfies each equation in the system. So, if an ordered pair is a solution, it will make both equations true.
![Page 4: CHAPTER 5 5-1 Solving Systems by Graphing. Objectives Identify solutions of linear equations in two variables. Solve systems of linear equations in two.](https://reader036.fdocuments.us/reader036/viewer/2022082816/56649ceb5503460f949b6eaa/html5/thumbnails/4.jpg)
Example#1
•Tell whether the ordered pair is a solution of the given system.
•(5, 2);
3x – y = 132 – 2 0
0 0
03(5) – 2 13
15 – 2 13
13 13
3x – y =13
The ordered pair (5, 2) makes both equations true.
(5, 2) is the solution of the system.
![Page 5: CHAPTER 5 5-1 Solving Systems by Graphing. Objectives Identify solutions of linear equations in two variables. Solve systems of linear equations in two.](https://reader036.fdocuments.us/reader036/viewer/2022082816/56649ceb5503460f949b6eaa/html5/thumbnails/5.jpg)
Example#2
•Tell whether the ordered pair is a solution of the given system.
•(–2, 2);•x + 3y = 4•–x + y = 2
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Solving Systems by Graphing
•All solutions of a linear equation are on its graph. To find a solution of a system of linear equations, you need a point that each line has in common. In other words, you need their point of intersection.
y = 2x – 1
y = –x + 5
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solution
•The point (2, 3) is where the two lines intersect and is a solution of both equations, so (2, 3) is the solution of the systems.
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Example
•Solve the system by graphing. Check your answer.
•y = x•y = –2x – 3
•The solution is (–1, –1).
![Page 9: CHAPTER 5 5-1 Solving Systems by Graphing. Objectives Identify solutions of linear equations in two variables. Solve systems of linear equations in two.](https://reader036.fdocuments.us/reader036/viewer/2022082816/56649ceb5503460f949b6eaa/html5/thumbnails/9.jpg)
Example
•Solve the system by graphing. Check your answer.
•y = x – 6
•y + 1/3 x = –1
![Page 10: CHAPTER 5 5-1 Solving Systems by Graphing. Objectives Identify solutions of linear equations in two variables. Solve systems of linear equations in two.](https://reader036.fdocuments.us/reader036/viewer/2022082816/56649ceb5503460f949b6eaa/html5/thumbnails/10.jpg)
Problem-solving Application
•Wren and Jenni are reading the same book. Wren is on page 14 and reads 2 pages every night. Jenni is on page 6 and reads 3 pages every night. After how many nights will they have read the same number of pages? How many pages will that be?
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Videos
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Student Guided Practice
•DO problems 2-7 in your book page 332
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Homework
Do problems 9-15 in your book page 332
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Closure
•Today we learned about solving systems of equations by graphing
•Next class we are going to learn about the substitution method.