It is required that we find an augmented matrix for the system.
Recall that a matrix that contains the coefficients and constant terms of a system of equations, each written in the standard form with the constant terms to the right of the equals is called an augmented matrix.
The given system of equations is:
[tex]\begin{cases}x+5y+8z=-9 \\ 3x+z=-4 \\ 7x+5y+7z=3\end{cases}[/tex]
The first, second, and third equations can be rewritten to get:
[tex]\begin{cases}1x+5y+8z=-9 \\ 3x+0y+1z=-4 \\ 7x+5y+7z=3\end{cases}[/tex]
Hence, the augmented matrix using the system is:
[tex]\begin{bmatrix}{1} & 5 & 8{|} & {-9} \\ {3} & {0} & {1|} & {-4} \\ {7} & {5} & {7|} & {3} \\ & {} & {} & {}\end{bmatrix}[/tex]
