1. The problem asks to write the augmented matrix for the system of linear equations: $$\begin{cases} 9x_1 + 6x_2 + 4x_3 = 8 \\ 7x_1 + x_2 - 9x_3 = 7 \end{cases}$$ 2. An augmented matrix combines the coefficients of the variables and the constants from the right side of the equations into one matrix. 3. For each equation, write the coefficients of $x_1$, $x_2$, and $x_3$ in order, then add the constant term as the last column. 4. The first equation coefficients are $9$, $6$, $4$ and the constant is $8$. 5. The second equation coefficients are $7$, $1$, $-9$ and the constant is $7$. 6. So the augmented matrix is: $$\left[ \begin{array}{ccc|c} 9 & 6 & 4 & 8 \\ 7 & 1 & -9 & 7 \end{array} \right]$$ 7. This matches option B, which is a $2 \times 4$ matrix (2 equations, 3 variables plus 1 augmented column). Final answer: The augmented matrix is $$\left[ \begin{array}{ccc|c} 9 & 6 & 4 & 8 \\ 7 & 1 & -9 & 7 \end{array} \right]$$