Answer:
The set of solutions is
![\{\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}12\\-7-r\\r\end{array}\right]: \text{r is a real number} \}](https://img.qammunity.org/2020/formulas/mathematics/college/66kun4rxis1wmy5r1j8cqqp4gcwqjwgwot.png)
Explanation:
The augmented matrix of the system is
.
We will use rows operations for find the echelon form of the matrix.
- In row 2 we subtract
from row 1. (R2- 2/3R1) and we obtain the matrix
![\left[\begin{array}{cccc}3&6&6&-9\\0&1&1&-7\end{array}\right]](https://img.qammunity.org/2020/formulas/mathematics/college/z5r8he2msykrf5st39t5xeehlp9w93s833.png)
- We multiply the row 1 by
.
Now we solve for the unknown variables:
The system has a free variable, the the system has infinite solutions and the set of solutions is
![\{\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}12\\-7-r\\r\end{array}\right]: \text{r is a real number} \}](https://img.qammunity.org/2020/formulas/mathematics/college/66kun4rxis1wmy5r1j8cqqp4gcwqjwgwot.png)