To determine [tex]\( D_y \)[/tex] for the given system of equations, we start by identifying what [tex]\( D_y \)[/tex] represents in the context of solving the system using determinants.
The system of equations provided is:
[tex]\[
\begin{array}{l}
2x - 3y = 17 \\
5x + 4y = 8
\end{array}
\][/tex]
When solving a system of linear equations using Cramer's Rule, [tex]\( D_y \)[/tex] is the determinant of the matrix formed by replacing the [tex]\( y \)[/tex]-column of the coefficient matrix with the constant terms from the equations.
1. The coefficient matrix for the given system is:
[tex]\[
\left[
\begin{array}{cc}
2 & -3 \\
5 & 4
\end{array}
\right]
\][/tex]
2. The constants from the right-hand side of the equations are:
[tex]\[
\left[
\begin{array}{c}
17 \\
8
\end{array}
\right]
\][/tex]
3. To find [tex]\( D_y \)[/tex], we replace the [tex]\( y \)[/tex]-column (the second column) in the original coefficient matrix with the constant terms:
[tex]\[
\left[
\begin{array}{cc}
2 & -3 \\
5 & 4
\end{array}
\right]
\rightarrow
\left[
\begin{array}{cc}
17 & -3 \\
8 & 4
\end{array}
\right]
\][/tex]
Therefore, the determinant of the matrix we need to find to determine [tex]\( D_y \)[/tex] is that of the matrix:
[tex]\[
\left[
\begin{array}{cc}
17 & -3 \\
8 & 4
\end{array}
\right]
\][/tex]
So the correct option is:
[tex]\[ \boxed{B} \][/tex]
