6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/badsubstitution.pdfconclusion the...
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![Page 1: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/1.jpg)
6x + 5y + 11z = 192x + 3y + 6z = 63x − 2y + 7z = 20
![Page 2: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/2.jpg)
6x + 5y + 11z = 192x + 3y + 6z = 63x − 2y + 7z = 20
x = 196 − 5
6 y − 116 z
![Page 3: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/3.jpg)
6x + 5y + 11z = 192x + 3y + 6z = 63x − 2y + 7z = 20
x = 196 − 5
6 y − 116 z
2( 19
6 − 56 y − 11
6 z)+ 3y + 6z = 6
![Page 4: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/4.jpg)
6x + 5y + 11z = 192x + 3y + 6z = 63x − 2y + 7z = 20
x = 196 − 5
6 y − 116 z
2( 19
6 − 56 y − 11
6 z)+ 3y + 6z = 6
43 y + 7
3 z = − 13
![Page 5: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/5.jpg)
6x + 5y + 11z = 192x + 3y + 6z = 63x − 2y + 7z = 20
x = 196 − 5
6 y − 116 z
2( 19
6 − 56 y − 11
6 z)+ 3y + 6z = 6
43 y + 7
3 z = − 13
y = − 74 z − 1
4
![Page 6: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/6.jpg)
6x + 5y + 11z = 192x + 3y + 6z = 63x − 2y + 7z = 20
x = 196 − 5
6 y − 116 z
2( 19
6 − 56 y − 11
6 z)+ 3y + 6z = 6
43 y + 7
3 z = − 13
y = − 74 z − 1
4
3( 19
6 − 56 y − 11
6 z)− 2y + 7z = 20
![Page 7: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/7.jpg)
6x + 5y + 11z = 192x + 3y + 6z = 63x − 2y + 7z = 20
x = 196 − 5
6 y − 116 z
2( 19
6 − 56 y − 11
6 z)+ 3y + 6z = 6
43 y + 7
3 z = − 13
y = − 74 z − 1
4
3( 19
6 − 56 y − 11
6 z)− 2y + 7z = 20
− 92 y + 3
2 z = 212
![Page 8: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/8.jpg)
6x + 5y + 11z = 192x + 3y + 6z = 63x − 2y + 7z = 20
x = 196 − 5
6 y − 116 z
2( 19
6 − 56 y − 11
6 z)+ 3y + 6z = 6
43 y + 7
3 z = − 13
y = − 74 z − 1
4
3( 19
6 − 56 y − 11
6 z)− 2y + 7z = 20
− 92 y + 3
2 z = 212
− 92
(− 7
4 z − 14
)+ 3
2 z = 212
![Page 9: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/9.jpg)
6x + 5y + 11z = 192x + 3y + 6z = 63x − 2y + 7z = 20
x = 196 − 5
6 y − 116 z
2( 19
6 − 56 y − 11
6 z)+ 3y + 6z = 6
43 y + 7
3 z = − 13
y = − 74 z − 1
4
3( 19
6 − 56 y − 11
6 z)− 2y + 7z = 20
− 92 y + 3
2 z = 212
− 92
(− 7
4 z − 14
)+ 3
2 z = 212 z = 1
![Page 10: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/10.jpg)
6x + 5y + 11z = 192x + 3y + 6z = 63x − 2y + 7z = 20
x = 196 − 5
6 y − 116 z
2( 19
6 − 56 y − 11
6 z)+ 3y + 6z = 6
43 y + 7
3 z = − 13
y = − 74 z − 1
4
3( 19
6 − 56 y − 11
6 z)− 2y + 7z = 20
− 92 y + 3
2 z = 212
− 92
(− 7
4 z − 14
)+ 3
2 z = 212 z = 1
y = −2
![Page 11: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/11.jpg)
6x + 5y + 11z = 192x + 3y + 6z = 63x − 2y + 7z = 20
x = 196 − 5
6 y − 116 z
2( 19
6 − 56 y − 11
6 z)+ 3y + 6z = 6
43 y + 7
3 z = − 13
y = − 74 z − 1
4
3( 19
6 − 56 y − 11
6 z)− 2y + 7z = 20
− 92 y + 3
2 z = 212
− 92
(− 7
4 z − 14
)+ 3
2 z = 212 z = 1
y = −2
x = 3
![Page 12: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/12.jpg)
Conclusion
The substitution method of solving systems of linearequations may work well if there are only 2 variables.If there are 3 or more variables, it can become a nightmare.
![Page 13: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/13.jpg)
Conclusion
The substitution method of solving systems of linearequations may work well if there are only 2 variables.If there are 3 or more variables, it can become a nightmare.
![Page 14: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/14.jpg)
![Page 15: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/15.jpg)
2x + 3y − 4z = 6−2x + y + 2z = 46x + 9y − 5z = 123x − 2y − 3z = 1
![Page 16: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/16.jpg)
2x + 3y − 4z = 6−2x + y + 2z = 46x + 9y − 5z = 123x − 2y − 3z = 1
2x + 3y − 4z = 6−2x + y + 2z = 4
4y − 2z = 10
![Page 17: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/17.jpg)
2x + 3y − 4z = 6−2x + y + 2z = 46x + 9y − 5z = 123x − 2y − 3z = 1
2x + 3y − 4z = 6−2x + y + 2z = 4
4y − 2z = 10
6x + 9y − 5z = 12−6x + 4y + 6z = −2
13y + z = 10
![Page 18: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/18.jpg)
2x + 3y − 4z = 6−2x + y + 2z = 46x + 9y − 5z = 123x − 2y − 3z = 1
2x + 3y − 4z = 6−2x + y + 2z = 4
4y − 2z = 10
6x + 9y − 5z = 12−6x + 4y + 6z = −2
13y + z = 10
4y − 2z = 1026y + 2z = 2030y = 30
![Page 19: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/19.jpg)
2x + 3y − 4z = 6−2x + y + 2z = 46x + 9y − 5z = 123x − 2y − 3z = 1
2x + 3y − 4z = 6−2x + y + 2z = 4
4y − 2z = 10
6x + 9y − 5z = 12−6x + 4y + 6z = −2
13y + z = 10
4y − 2z = 1026y + 2z = 2030y = 30
y = 1
![Page 20: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/20.jpg)
2x + 3y − 4z = 6−2x + y + 2z = 46x + 9y − 5z = 123x − 2y − 3z = 1
2x + 3y − 4z = 6−2x + y + 2z = 4
4y − 2z = 10
6x + 9y − 5z = 12−6x + 4y + 6z = −2
13y + z = 10
4y − 2z = 1026y + 2z = 2030y = 30
y = 1z = 10 − 13y
![Page 21: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/21.jpg)
2x + 3y − 4z = 6−2x + y + 2z = 46x + 9y − 5z = 123x − 2y − 3z = 1
2x + 3y − 4z = 6−2x + y + 2z = 4
4y − 2z = 10
6x + 9y − 5z = 12−6x + 4y + 6z = −2
13y + z = 10
4y − 2z = 1026y + 2z = 2030y = 30
y = 1z = 10 − 13y
z = −3
![Page 22: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/22.jpg)
2x + 3y − 4z = 6−2x + y + 2z = 46x + 9y − 5z = 123x − 2y − 3z = 1
2x + 3y − 4z = 6−2x + y + 2z = 4
4y − 2z = 10
6x + 9y − 5z = 12−6x + 4y + 6z = −2
13y + z = 10
4y − 2z = 1026y + 2z = 2030y = 30
y = 1z = 10 − 13y
z = −3
x = 16 (12 − 9y + 5z)
![Page 23: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/23.jpg)
2x + 3y − 4z = 6−2x + y + 2z = 46x + 9y − 5z = 123x − 2y − 3z = 1
2x + 3y − 4z = 6−2x + y + 2z = 4
4y − 2z = 10
6x + 9y − 5z = 12−6x + 4y + 6z = −2
13y + z = 10
4y − 2z = 1026y + 2z = 2030y = 30
y = 1z = 10 − 13y
z = −3
x = 16 (12 − 9y + 5z) x = −2
![Page 24: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/24.jpg)
2x + 3y − 4z = 6−2x + y + 2z = 46x + 9y − 5z = 123x − 2y − 3z = 1
2x + 3y − 4z = 6−2x + y + 2z = 4
4y − 2z = 10
6x + 9y − 5z = 12−6x + 4y + 6z = −2
13y + z = 10
4y − 2z = 1026y + 2z = 2030y = 30
y = 1z = 10 − 13y
z = −3
x = 16 (12 − 9y + 5z) x = −2
2x + 3y − 4z ?= 6
![Page 25: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/25.jpg)
2x + 3y − 4z = 6−2x + y + 2z = 46x + 9y − 5z = 123x − 2y − 3z = 1
2x + 3y − 4z = 6−2x + y + 2z = 4
4y − 2z = 10
6x + 9y − 5z = 12−6x + 4y + 6z = −2
13y + z = 10
4y − 2z = 1026y + 2z = 2030y = 30
y = 1z = 10 − 13y
z = −3
x = 16 (12 − 9y + 5z) x = −2
2x + 3y − 4z ?= 6
2(−2) + 3(1)− 4(−3) = 11
![Page 26: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/26.jpg)
2x + 3y − 4z = 6−2x + y + 2z = 46x + 9y − 5z = 123x − 2y − 3z = 1
2x + 3y − 4z = 6−2x + y + 2z = 4
4y − 2z = 10
6x + 9y − 5z = 12−6x + 4y + 6z = −2
13y + z = 10
4y − 2z = 1026y + 2z = 2030y = 30
y = 1z = 10 − 13y
z = −3
x = 16 (12 − 9y + 5z) x = −2
2x + 3y − 4z ?= 6
2(−2) + 3(1)− 4(−3) = 11
???
![Page 27: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/27.jpg)
Conclusion
The addition method of solving systems of linearequations sometimes works well if there are only 2 or 3equations.However, it’s easy to get lost if you don’t keep organized.Far worse, if you just work haphazardly, you can get wronganswers!
![Page 28: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/28.jpg)
Conclusion
The addition method of solving systems of linearequations sometimes works well if there are only 2 or 3equations.However, it’s easy to get lost if you don’t keep organized.Far worse, if you just work haphazardly, you can get wronganswers!
![Page 29: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/29.jpg)
Conclusion
The addition method of solving systems of linearequations sometimes works well if there are only 2 or 3equations.However, it’s easy to get lost if you don’t keep organized.Far worse, if you just work haphazardly, you can get wronganswers!
![Page 30: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/30.jpg)
What We Want
Our DesireWe want a system for solving systems of linear equations that
produces all solutions to the system.never produces fake solutions.is systematic and organized.never requires guesswork to know the next move.
![Page 31: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/31.jpg)
What We Want
Our DesireWe want a system for solving systems of linear equations that
produces all solutions to the system.never produces fake solutions.is systematic and organized.never requires guesswork to know the next move.
![Page 32: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/32.jpg)
What We Want
Our DesireWe want a system for solving systems of linear equations that
produces all solutions to the system.never produces fake solutions.is systematic and organized.never requires guesswork to know the next move.
![Page 33: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/33.jpg)
What We Want
Our DesireWe want a system for solving systems of linear equations that
produces all solutions to the system.never produces fake solutions.is systematic and organized.never requires guesswork to know the next move.
![Page 34: 6x 5y 11z 19 x 3y 6z 6 3x 2y 7z 20faculty.cord.edu/ahendric/210/BadSubstitution.pdfConclusion The substitution method of solving systems of linear](https://reader031.vdocuments.site/reader031/viewer/2022020109/5ba68a0809d3f22f1b8bdafd/html5/thumbnails/34.jpg)
What We Want
Our DesireWe want a system for solving systems of linear equations that
produces all solutions to the system.never produces fake solutions.is systematic and organized.never requires guesswork to know the next move.