Final answer:
The augmented matrix for the given system of equations is \(\begin{bmatrix} 9 & -8 & | & -6 \\ 4 & 2 & | & -5 \end{bmatrix}\). It is organized with coefficients of x and y in the first and second columns, and constants in the third column.
Step-by-step explanation:
The augmented matrix for the system of equations provided can be found by arranging the coefficients of the variables along with the constants in a matrix form. The system given is:
\(9x - 8y = -6\)
\(4x + 2y = -5\)
The corresponding augmented matrix is:
\(\begin{bmatrix} 9 & -8 & | & -6 \\ 4 & 2 & | & -5 \end{bmatrix}\)
In this matrix, the first row represents the coefficients and constant term of the first equation, while the second row represents those of the second equation, with the vertical bar separating the coefficients from the constants.