3. Determine whether the system of equations has a unique solution. If it does then solve for $y$.
If there is no answer, write "none" in the box.
\[
\begin{array}{l}
10 x+5 y-2 z=132 \\
-1 x-6 y+2 z=-46 \\
5 x-2 y-3 z=60
\end{array}
\]
\[
y=
\]

Step 1 ：The system of equations is a linear system with three variables. To determine whether the system has a unique solution, we can use the determinant method. If the determinant of the coefficient matrix is not zero, then the system has a unique solution. If the determinant is zero, then the system does not have a unique solution.

Step 2 ：To solve for y, we can use Cramer's Rule. Cramer's Rule states that the solution to a system of linear equations can be found by finding the determinants of certain matrices derived from the system of equations.

Step 3 ：Let's calculate the determinant of the coefficient matrix and if it's not zero, we'll use Cramer's Rule to solve for y.

Step 4 ：The determinant of the coefficient matrix is \(191.0\), which is not zero. This means the system of equations has a unique solution.

Step 5 ：Using Cramer's Rule, we find that the determinant of the matrix with the y-column replaced by the solution vector is \(763.9999999999994\).

Step 6 ：Finally, we divide this determinant by the determinant of the coefficient matrix to find the value of y, which is approximately \(4\).

Step 7 ：Final Answer: The system of equations has a unique solution and the value of \(y\) is \(\boxed{4}\).