Types of Linear Systems. Background In slope-intercept form, the equation of a line is given by the...
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![Page 1: Types of Linear Systems. Background In slope-intercept form, the equation of a line is given by the form: y = mx + b m represents what? b represents what?](https://reader036.fdocuments.net/reader036/viewer/2022081404/5a4d1ba27f8b9ab0599c7fa3/html5/thumbnails/1.jpg)
Types of Linear Systems
![Page 2: Types of Linear Systems. Background In slope-intercept form, the equation of a line is given by the form: y = mx + b m represents what? b represents what?](https://reader036.fdocuments.net/reader036/viewer/2022081404/5a4d1ba27f8b9ab0599c7fa3/html5/thumbnails/2.jpg)
Background
In slope-intercept form, the equation of a line is given by the form:
y = mx + b
m represents what?
b represents what?
![Page 3: Types of Linear Systems. Background In slope-intercept form, the equation of a line is given by the form: y = mx + b m represents what? b represents what?](https://reader036.fdocuments.net/reader036/viewer/2022081404/5a4d1ba27f8b9ab0599c7fa3/html5/thumbnails/3.jpg)
Introduction
A system of linear equations consists of two or more linear equations graphed on the same coordinate plane.
In this presentation, we will be looking at systems with two linear equations.
![Page 4: Types of Linear Systems. Background In slope-intercept form, the equation of a line is given by the form: y = mx + b m represents what? b represents what?](https://reader036.fdocuments.net/reader036/viewer/2022081404/5a4d1ba27f8b9ab0599c7fa3/html5/thumbnails/4.jpg)
IntroductionAll three types of systems of linear
equations we will discuss can be seen in this picture:
There are three types of systems of linear equations:
•Systems with no solution
•Systems with exactly one solution
•Systems with infinitely many solutions
![Page 5: Types of Linear Systems. Background In slope-intercept form, the equation of a line is given by the form: y = mx + b m represents what? b represents what?](https://reader036.fdocuments.net/reader036/viewer/2022081404/5a4d1ba27f8b9ab0599c7fa3/html5/thumbnails/5.jpg)
System with No Solution
In the picture, the highlighted rails are like lines that do not intersect as they are parallel.
A system with no solution is a system in which the graphs do not cross or touch anywhere. In other words, the graphs do not intersect; they are parallel.
A system with no solution is sometimes referred to as an inconsistent system.
![Page 6: Types of Linear Systems. Background In slope-intercept form, the equation of a line is given by the form: y = mx + b m represents what? b represents what?](https://reader036.fdocuments.net/reader036/viewer/2022081404/5a4d1ba27f8b9ab0599c7fa3/html5/thumbnails/6.jpg)
System with No Solution
The picture to the right is an example of a system with no solution.
![Page 7: Types of Linear Systems. Background In slope-intercept form, the equation of a line is given by the form: y = mx + b m represents what? b represents what?](https://reader036.fdocuments.net/reader036/viewer/2022081404/5a4d1ba27f8b9ab0599c7fa3/html5/thumbnails/7.jpg)
System with Exactly One Solution
In the picture, the highlighted rails are like lines that cross at exactly one place.
A system with exactly one solution is a system in which the graphs cross or touch at exactly one place.
A system with exactly one solution is sometimes referred to as an independent system.
![Page 8: Types of Linear Systems. Background In slope-intercept form, the equation of a line is given by the form: y = mx + b m represents what? b represents what?](https://reader036.fdocuments.net/reader036/viewer/2022081404/5a4d1ba27f8b9ab0599c7fa3/html5/thumbnails/8.jpg)
System with Exactly One Solution
The picture to the right is an example of a system with exactly one solution.
![Page 9: Types of Linear Systems. Background In slope-intercept form, the equation of a line is given by the form: y = mx + b m represents what? b represents what?](https://reader036.fdocuments.net/reader036/viewer/2022081404/5a4d1ba27f8b9ab0599c7fa3/html5/thumbnails/9.jpg)
System with Infinitely Many Solutions
In the picture, the highlighted rail looks like one line. The graph of a system with infinitely many solutions will look like one line when graphed.
A system with infinitely many solutions consists of the same line twice. In other words, the lines overlap everywhere.
A system with infinitely many solutions is sometimes referred to as a dependent system.
![Page 10: Types of Linear Systems. Background In slope-intercept form, the equation of a line is given by the form: y = mx + b m represents what? b represents what?](https://reader036.fdocuments.net/reader036/viewer/2022081404/5a4d1ba27f8b9ab0599c7fa3/html5/thumbnails/10.jpg)
System with Infinitely Many Solutions
The picture to the right is an example of a system with infinitely many solutions.
![Page 11: Types of Linear Systems. Background In slope-intercept form, the equation of a line is given by the form: y = mx + b m represents what? b represents what?](https://reader036.fdocuments.net/reader036/viewer/2022081404/5a4d1ba27f8b9ab0599c7fa3/html5/thumbnails/11.jpg)
Enrichment
Do you see examples of systems of equations in the picture to the right?
![Page 12: Types of Linear Systems. Background In slope-intercept form, the equation of a line is given by the form: y = mx + b m represents what? b represents what?](https://reader036.fdocuments.net/reader036/viewer/2022081404/5a4d1ba27f8b9ab0599c7fa3/html5/thumbnails/12.jpg)
Enrichment
Do you see examples of systems of equations in the picture to the right?
![Page 13: Types of Linear Systems. Background In slope-intercept form, the equation of a line is given by the form: y = mx + b m represents what? b represents what?](https://reader036.fdocuments.net/reader036/viewer/2022081404/5a4d1ba27f8b9ab0599c7fa3/html5/thumbnails/13.jpg)
Enrichment
Do you see examples of systems of equations in the picture to the right?
![Page 14: Types of Linear Systems. Background In slope-intercept form, the equation of a line is given by the form: y = mx + b m represents what? b represents what?](https://reader036.fdocuments.net/reader036/viewer/2022081404/5a4d1ba27f8b9ab0599c7fa3/html5/thumbnails/14.jpg)
Summary• What does it mean if a system of linear equations has no
solution?
• What does it mean if a system of linear equations has exactly one solution?
• What does it mean if a system of linear equations has infinitely many solutions?