6.1 – graphing systems of equations
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6.1 – Graphing Systems of Equations. Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. - PowerPoint PPT PresentationTRANSCRIPT
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6.1 – Graphing Systems of Equations
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Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions.
![Page 3: 6.1 – Graphing Systems of Equations](https://reader033.vdocuments.mx/reader033/viewer/2022051623/56815a95550346895dc81335/html5/thumbnails/3.jpg)
Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions.
a. y = -x + 1
y = x – 3
y = -x + 1
y = x – 3y = -x – 2
![Page 4: 6.1 – Graphing Systems of Equations](https://reader033.vdocuments.mx/reader033/viewer/2022051623/56815a95550346895dc81335/html5/thumbnails/4.jpg)
Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions.
a. y = -x + 1
y = x – 3
y = -x + 1
y = x – 3y = -x – 2
![Page 5: 6.1 – Graphing Systems of Equations](https://reader033.vdocuments.mx/reader033/viewer/2022051623/56815a95550346895dc81335/html5/thumbnails/5.jpg)
Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions.
a. y = -x + 1
y = x – 3
y = -x + 1
y = x – 3y = -x – 2
![Page 6: 6.1 – Graphing Systems of Equations](https://reader033.vdocuments.mx/reader033/viewer/2022051623/56815a95550346895dc81335/html5/thumbnails/6.jpg)
Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions.
a. y = -x + 1
y = x – 3
y = -x + 1
y = x – 3y = -x – 2
![Page 7: 6.1 – Graphing Systems of Equations](https://reader033.vdocuments.mx/reader033/viewer/2022051623/56815a95550346895dc81335/html5/thumbnails/7.jpg)
Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions.
a. y = -x + 1
y = x – 3
y = -x + 1
y = x – 3y = -x – 2
![Page 8: 6.1 – Graphing Systems of Equations](https://reader033.vdocuments.mx/reader033/viewer/2022051623/56815a95550346895dc81335/html5/thumbnails/8.jpg)
Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions.
a. y = -x + 1
y = x – 3
y = -x + 1
y = x – 3y = -x – 2
![Page 9: 6.1 – Graphing Systems of Equations](https://reader033.vdocuments.mx/reader033/viewer/2022051623/56815a95550346895dc81335/html5/thumbnails/9.jpg)
Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions.
a. y = -x + 1
y = x – 3
One Sol.
y = -x + 1
y = x – 3y = -x – 2
![Page 10: 6.1 – Graphing Systems of Equations](https://reader033.vdocuments.mx/reader033/viewer/2022051623/56815a95550346895dc81335/html5/thumbnails/10.jpg)
Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions.
a. y = -x + 1
y = x – 3
One Sol.
b. y = -x + 1
2y = -2x – 4
y = -x + 1
y = x – 3y = -x – 2
![Page 11: 6.1 – Graphing Systems of Equations](https://reader033.vdocuments.mx/reader033/viewer/2022051623/56815a95550346895dc81335/html5/thumbnails/11.jpg)
Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions.
a. y = -x + 1
y = x – 3
One Sol.
b. y = -x + 1
2y = -2x – 4
y = -x + 1
y = x – 3y = -x – 2
![Page 12: 6.1 – Graphing Systems of Equations](https://reader033.vdocuments.mx/reader033/viewer/2022051623/56815a95550346895dc81335/html5/thumbnails/12.jpg)
Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions.
a. y = -x + 1
y = x – 3
One Sol.
b. y = -x + 1
2y = -2x – 4
y = -x + 1
y = x – 3y = -x – 2
![Page 13: 6.1 – Graphing Systems of Equations](https://reader033.vdocuments.mx/reader033/viewer/2022051623/56815a95550346895dc81335/html5/thumbnails/13.jpg)
Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions.
a. y = -x + 1
y = x – 3
One Sol.
b. y = -x + 1
2y = -2x – 4
2 2 2
y = -x + 1
y = x – 3y = -x – 2
![Page 14: 6.1 – Graphing Systems of Equations](https://reader033.vdocuments.mx/reader033/viewer/2022051623/56815a95550346895dc81335/html5/thumbnails/14.jpg)
Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions.
a. y = -x + 1
y = x – 3
One Sol.
b. y = -x + 1
y = -x – 2
y = -x + 1
y = x – 3y = -x – 2
![Page 15: 6.1 – Graphing Systems of Equations](https://reader033.vdocuments.mx/reader033/viewer/2022051623/56815a95550346895dc81335/html5/thumbnails/15.jpg)
Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions.
a. y = -x + 1
y = x – 3
One Sol.
b. y = -x + 1
y = -x – 2
y = -x + 1
y = x – 3y = -x – 2
![Page 16: 6.1 – Graphing Systems of Equations](https://reader033.vdocuments.mx/reader033/viewer/2022051623/56815a95550346895dc81335/html5/thumbnails/16.jpg)
Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions.
a. y = -x + 1
y = x – 3
One Sol.
b. y = -x + 1
y = -x – 2
y = -x + 1
y = x – 3y = -x – 2
![Page 17: 6.1 – Graphing Systems of Equations](https://reader033.vdocuments.mx/reader033/viewer/2022051623/56815a95550346895dc81335/html5/thumbnails/17.jpg)
Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions.
a. y = -x + 1
y = x – 3
One Sol.
b. y = -x + 1
y = -x – 2
No Sol.
y = -x + 1
y = x – 3y = -x – 2
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Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions.a. y = -x + 1 y = x – 3
One Sol.b. y = -x + 1
y = -x – 2 No Sol. c. 2y = -2x – 4 y = -x – 2
y = -x + 1
y = x – 3y = -x – 2
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Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions.a. y = -x + 1 y = x – 3
One Sol.b. y = -x + 1
y = -x – 2 No Sol. c. 2y = -2x – 4 y = -x – 2
y = -x + 1
y = x – 3y = -x – 2
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Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions.a. y = -x + 1 y = x – 3
One Sol.b. y = -x + 1
y = -x – 2 No Sol. c. 2y = -2x – 4
2 2 2 y = -x – 2
y = -x + 1
y = x – 3y = -x – 2
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Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions.a. y = -x + 1 y = x – 3
One Sol.b. y = -x + 1
y = -x – 2 No Sol. c. y = -x – 2 y = -x – 2
y = -x + 1
y = x – 3y = -x – 2
![Page 22: 6.1 – Graphing Systems of Equations](https://reader033.vdocuments.mx/reader033/viewer/2022051623/56815a95550346895dc81335/html5/thumbnails/22.jpg)
Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions.a. y = -x + 1 y = x – 3
One Sol.b. y = -x + 1
y = -x – 2 No Sol. c. y = -x – 2 y = -x – 2
y = -x + 1
y = x – 3y = -x – 2
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Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions.a. y = -x + 1 y = x – 3
One Sol.b. y = -x + 1
y = -x – 2 No Sol. c. y = -x – 2 y = -x – 2
y = -x + 1
y = x – 3y = -x – 2
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Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions.a. y = -x + 1 y = x – 3
One Sol.b. y = -x + 1
y = -x – 2 No Sol. c. y = -x – 2 y = -x – 2
y = -x + 1
y = x – 3y = -x – 2
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Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions.a. y = -x + 1 y = x – 3
One Sol.b. y = -x + 1
y = -x – 2 No Sol. c. y = -x – 2 y = -x – 2
Infinite Sol.
y = -x + 1
y = x – 3y = -x – 2
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Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it.
a. y = 2x – 1
y = -2x – 1
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Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it.
a. y = 2x – 1
m = 2
y = -2x – 1
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Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it.
a. y = 2x – 1
m = 2, b = -1
y = -2x – 1
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Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it.
a. y = 2x – 1
m = 2, b = -1
y = -2x – 1
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Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it.
a. y = 2x – 1
m = 2, b = -1
y = -2x – 1
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Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it.
a. y = 2x – 1
m = 2, b = -1
y = -2x – 1
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Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it.
a. y = 2x – 1
m = 2, b = -1
y = -2x – 1
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Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it.
a. y = 2x – 1
m = 2, b = -1
y = -2x – 1
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Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it.
a. y = 2x – 1
m = 2, b = -1
y = -2x – 1
m = -2
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Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it.
a. y = 2x – 1
m = 2, b = -1
y = -2x – 1
m = -2, b = -1
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Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it.
a. y = 2x – 1
m = 2, b = -1
y = -2x – 1
m = -2, b = -1
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Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it.
a. y = 2x – 1
m = 2, b = -1
y = -2x – 1
m = -2, b = -1
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Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it.
a. y = 2x – 1
m = 2, b = -1
y = -2x – 1
m = -2, b = -1
![Page 39: 6.1 – Graphing Systems of Equations](https://reader033.vdocuments.mx/reader033/viewer/2022051623/56815a95550346895dc81335/html5/thumbnails/39.jpg)
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it.
a. y = 2x – 1
m = 2, b = -1
y = -2x – 1
m = -2, b = -1
![Page 40: 6.1 – Graphing Systems of Equations](https://reader033.vdocuments.mx/reader033/viewer/2022051623/56815a95550346895dc81335/html5/thumbnails/40.jpg)
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it.
a. y = 2x – 1
m = 2, b = -1
y = -2x – 1
m = -2, b = -1
![Page 41: 6.1 – Graphing Systems of Equations](https://reader033.vdocuments.mx/reader033/viewer/2022051623/56815a95550346895dc81335/html5/thumbnails/41.jpg)
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it.
a. y = 2x – 1
m = 2, b = -1
y = -2x – 1
m = -2, b = -1
One sol. @ (0,-1)
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b. 2x + 3y = 6
-4x – 6y = -12
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b. 2x + 3y = 6
3y = -2x + 6
-4x – 6y = -12
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b. 2x + 3y = 6
3y = -2x + 6
y = -⅔x + 2
-4x – 6y = -12
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b. 2x + 3y = 6
3y = -2x + 6
y = -⅔x + 2
m = -2
3
-4x – 6y = -12
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b. 2x + 3y = 6
3y = -2x + 6
y = -⅔x + 2
m = -2 , b = 2
3
-4x – 6y = -12
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b. 2x + 3y = 6
3y = -2x + 6
y = -⅔x + 2
m = -2 , b = 2
3
-4x – 6y = -12
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b. 2x + 3y = 6
3y = -2x + 6
y = -⅔x + 2
m = -2 , b = 2
3
-4x – 6y = -12
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b. 2x + 3y = 6
3y = -2x + 6
y = -⅔x + 2
m = -2 , b = 2
3
-4x – 6y = -12
![Page 50: 6.1 – Graphing Systems of Equations](https://reader033.vdocuments.mx/reader033/viewer/2022051623/56815a95550346895dc81335/html5/thumbnails/50.jpg)
b. 2x + 3y = 6
3y = -2x + 6
y = -⅔x + 2
m = -2 , b = 2
3
-4x – 6y = -12
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b. 2x + 3y = 6
3y = -2x + 6
y = -⅔x + 2
m = -2 , b = 2
3
-4x – 6y = -12
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b. 2x + 3y = 6
3y = -2x + 6
y = -⅔x + 2
m = -2 , b = 2
3
-4x – 6y = -12
-6y = 4x – 12
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b. 2x + 3y = 6
3y = -2x + 6
y = -⅔x + 2
m = -2 , b = 2
3
-4x – 6y = -12
-6y = 4x – 12
y = -⅔x + 2
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b. 2x + 3y = 6
3y = -2x + 6
y = -⅔x + 2
m = -2 , b = 2
3
-4x – 6y = -12
-6y = 4x – 12
y = -⅔x + 2
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b. 2x + 3y = 6
3y = -2x + 6
y = -⅔x + 2
m = -2 , b = 2
3
-4x – 6y = -12
-6y = 4x – 12
y = -⅔x + 2
Same line, therefore infinite sol.
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c. 2x + y = 1
y = -2x – 1
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c. 2x + y = 1
y = -2x + 1
m = -2, b = 1
y = -2x – 1
m = -2, b = -1
Parallel lines, therefore no sol.