17. Which expression represents $y$ in the system below? \[ \begin{array}{l} 3 x-8 y=-21 \\ 8 x+3 y=17 \end{array} \] $\frac{\left|\begin{array}{cc}-21 & -8 \\ 17 & 3\end{array}\right|}{\left|\begin{array}{cc}3 & -8 \\ 8 & 3\end{array}\right|}$ $\frac{\left|\begin{array}{cc}3 & -8 \\ 8 & 3\end{array}\right|}{\left|\begin{array}{cc}-21 & -8 \\ 17 & 3\end{array}\right|}$ $\frac{\left|\begin{array}{cc}3 & -8 \\ 8 & 3\end{array}\right|}{\left|\begin{array}{cc}3 & -21 \\ 8 & 17\end{array}\right|}$ $\frac{\left|\begin{array}{cc}3 & -21 \\ 8 & 17\end{array}\right|}{\left|\begin{array}{cc}3 & -8 \\ 8 & 3\end{array}\right|}$

Step 1 ：The question is asking for the value of $y$ in the given system of equations. This can be solved using Cramer's rule. According to Cramer's rule, the value of a variable is the ratio of the determinant of a matrix obtained by replacing the coefficients of the variable in the coefficient matrix with the constants in the system to the determinant of the coefficient matrix.

Step 2 ：In this case, to find $y$, we replace the coefficients of $y$ in the coefficient matrix with the constants in the system. The determinant of this new matrix divided by the determinant of the coefficient matrix gives the value of $y$.

Step 3 ：The coefficient matrix is \[\begin{array}{cc}3 & -8 \\8 & 3\end{array}\]

Step 4 ：The matrix obtained by replacing the coefficients of $y$ with the constants is \[\begin{array}{cc}3 & -21 \\8 & 17\end{array}\]

Step 5 ：So, the expression for $y$ is \[\frac{\left|\begin{array}{cc}3 & -21 \\8 & 17\end{array}\right|}{\left|\begin{array}{cc}3 & -8 \\8 & 3\end{array}\right|}\]

Step 6 ：The value of $y$ is approximately 3. This is consistent with the expression for $y$ that we derived using Cramer's rule.

Step 7 ：Final Answer: The expression that represents $y$ in the system is \[\boxed{\frac{\left|\begin{array}{cc}3 & -21 \\8 & 17\end{array}\right|}{\left|\begin{array}{cc}3 & -8 \\8 & 3\end{array}\right|}}\]