Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Ask your questions and receive accurate answers from professionals with extensive experience in various fields on our platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
Let's match each system of equations to its solution represented by an augmented matrix.
### Systems of Equations and Solutions:
1. System 1:
[tex]\[ \begin{array}{c} x + y + z = 1,100 \\ x - 2y - z = -500 \\ 2x + 3y + 2z = 2,600 \end{array} \][/tex]
Solution:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 750 \\ 0 & 1 & 0 & 850 \\ 0 & 0 & 1 & 1,000 \end{array}\right] \][/tex]
2. System 2:
[tex]\[ \begin{array}{c} x + y + z = 2,600 \\ x + y - z = 600 \\ 2x + y + 2z = 3,050 \end{array} \][/tex]
Solution:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 1,300 \\ 0 & 1 & 0 & 1,100 \\ 0 & 0 & 1 & 900 \end{array}\right] \][/tex]
3. System 3:
[tex]\[ \begin{array}{c} x + y + z = 1,900 \\ x - y - 2z = -2,000 \\ 2x + 2y + z = 1,100 \end{array} \][/tex]
Solution:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 500 \\ 0 & 1 & 0 & 400 \\ 0 & 0 & 1 & 200 \end{array}\right] \][/tex]
4. System 4:
[tex]\[ \begin{array}{c} x + y + z = 1,900 \\ x - y - 2z = -2,000 \\ 2x + 2y + z = 2,900 \end{array} \][/tex]
Solution:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 400 \\ 0 & 1 & 0 & 600 \\ 0 & 0 & 1 & 900 \end{array}\right] \][/tex]
5. System 5:
[tex]\[ \begin{array}{c} x + y + z = 3,300 \\ x + y - z = 1,500 \\ 2x + 3y + 2z = 7,700 \end{array} \][/tex]
Solution:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 1300 \\ 0 & 1 & 0 & 1100 \\ 0 & 0 & 1 & 900 \end{array}\right] \][/tex]
### Matching:
- [tex]\(\left[\begin{array}{ccc|c}1 & 0 & 0 & 750 \\ 0 & 1 & 0 & 850 \\ 0 & 0 & 1 & 1,000\end{array}\right]\)[/tex] matches with:
* [tex]\(\begin{array}{c} x+y+z=1,100 \\ x-2 y-z=-500 \\ 2 x+3 y+2z=2,600 \end{array}\)[/tex]
- [tex]\(\left[\begin{array}{ccc|c}1 & 0 & 0 & 1,300 \\ 0 & 1 & 0 & 1,100 \\ 0 & 0 & 1 & 900\end{array}\right]\)[/tex] matches with:
* [tex]\(\begin{array}{c} x+y+z=2,600 \\ x+y-z=600 \\ 2 x+y+2 z=3,050 \end{array}\)[/tex]
- [tex]\(\left[\begin{array}{ccc|c}1 & 0 & 0 & 500 \\ 0 & 1 & 0 & 400 \\ 0 & 0 & 1 & 200\end{array}\right]\)[/tex] matches with:
* [tex]\(\begin{array}{c} x+y+z=1,900 \\ x-y-2 z=-2,000 \\ 2 x+2y+z=1,100 \end{array}\)[/tex]
- [tex]\(\left[\begin{array}{ccc|c}1 & 0 & 0 & 400 \\ 0 & 1 & 0 & 600 \\ 0 & 0 & 1 & 900\end{array}\right]\)[/tex] matches with:
* [tex]\(\begin{array}{c} x+y+z=1,900 \\ x-y-2 z=-2,000 \\ 2x+2y+z=2,900 \end{array}\)[/tex]
- [tex]\(\left[\begin{array}{ccc|c}1 & 0 & 0 & 1,300 \\ 0 & 1 & 0 & 1,100 \\ 0 & 0 & 1 & 900\end{array}\right]\)[/tex] matches with:
* [tex]\(\begin{array}{c} x+y+z=3,300 \\ x+y-z=1,500 \\ 2 x+3 y+2 z=7,700 \end{array}\)[/tex]
These are the correct matchings between the systems of equations and their solutions.
### Systems of Equations and Solutions:
1. System 1:
[tex]\[ \begin{array}{c} x + y + z = 1,100 \\ x - 2y - z = -500 \\ 2x + 3y + 2z = 2,600 \end{array} \][/tex]
Solution:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 750 \\ 0 & 1 & 0 & 850 \\ 0 & 0 & 1 & 1,000 \end{array}\right] \][/tex]
2. System 2:
[tex]\[ \begin{array}{c} x + y + z = 2,600 \\ x + y - z = 600 \\ 2x + y + 2z = 3,050 \end{array} \][/tex]
Solution:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 1,300 \\ 0 & 1 & 0 & 1,100 \\ 0 & 0 & 1 & 900 \end{array}\right] \][/tex]
3. System 3:
[tex]\[ \begin{array}{c} x + y + z = 1,900 \\ x - y - 2z = -2,000 \\ 2x + 2y + z = 1,100 \end{array} \][/tex]
Solution:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 500 \\ 0 & 1 & 0 & 400 \\ 0 & 0 & 1 & 200 \end{array}\right] \][/tex]
4. System 4:
[tex]\[ \begin{array}{c} x + y + z = 1,900 \\ x - y - 2z = -2,000 \\ 2x + 2y + z = 2,900 \end{array} \][/tex]
Solution:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 400 \\ 0 & 1 & 0 & 600 \\ 0 & 0 & 1 & 900 \end{array}\right] \][/tex]
5. System 5:
[tex]\[ \begin{array}{c} x + y + z = 3,300 \\ x + y - z = 1,500 \\ 2x + 3y + 2z = 7,700 \end{array} \][/tex]
Solution:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 1300 \\ 0 & 1 & 0 & 1100 \\ 0 & 0 & 1 & 900 \end{array}\right] \][/tex]
### Matching:
- [tex]\(\left[\begin{array}{ccc|c}1 & 0 & 0 & 750 \\ 0 & 1 & 0 & 850 \\ 0 & 0 & 1 & 1,000\end{array}\right]\)[/tex] matches with:
* [tex]\(\begin{array}{c} x+y+z=1,100 \\ x-2 y-z=-500 \\ 2 x+3 y+2z=2,600 \end{array}\)[/tex]
- [tex]\(\left[\begin{array}{ccc|c}1 & 0 & 0 & 1,300 \\ 0 & 1 & 0 & 1,100 \\ 0 & 0 & 1 & 900\end{array}\right]\)[/tex] matches with:
* [tex]\(\begin{array}{c} x+y+z=2,600 \\ x+y-z=600 \\ 2 x+y+2 z=3,050 \end{array}\)[/tex]
- [tex]\(\left[\begin{array}{ccc|c}1 & 0 & 0 & 500 \\ 0 & 1 & 0 & 400 \\ 0 & 0 & 1 & 200\end{array}\right]\)[/tex] matches with:
* [tex]\(\begin{array}{c} x+y+z=1,900 \\ x-y-2 z=-2,000 \\ 2 x+2y+z=1,100 \end{array}\)[/tex]
- [tex]\(\left[\begin{array}{ccc|c}1 & 0 & 0 & 400 \\ 0 & 1 & 0 & 600 \\ 0 & 0 & 1 & 900\end{array}\right]\)[/tex] matches with:
* [tex]\(\begin{array}{c} x+y+z=1,900 \\ x-y-2 z=-2,000 \\ 2x+2y+z=2,900 \end{array}\)[/tex]
- [tex]\(\left[\begin{array}{ccc|c}1 & 0 & 0 & 1,300 \\ 0 & 1 & 0 & 1,100 \\ 0 & 0 & 1 & 900\end{array}\right]\)[/tex] matches with:
* [tex]\(\begin{array}{c} x+y+z=3,300 \\ x+y-z=1,500 \\ 2 x+3 y+2 z=7,700 \end{array}\)[/tex]
These are the correct matchings between the systems of equations and their solutions.
We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.
