Determine the solution to the given system of linear equations, by creating an augmented matrix and using Gauss-Jordan elimination to convert it to reduced row echelon form. Then enter the solution* of $y$ in the box. *If there is a free variable, set $z=t$ and if the system is inconsistent type "inconsistent" in the box. \[ \begin{array}{l} -7 x+4 y-22 z=-6 \\ 8 x-3 y+33 z=10 \\ 2 x-6 y-18 z=-8 \end{array} \]

Step 1 ：Create an augmented matrix from the given system of equations. The augmented matrix is a matrix that includes the coefficients of the variables and the constants on the other side of the equal sign. The rows of the matrix represent the equations, and the columns represent the variables.

Step 2 ：Use Gauss-Jordan elimination to convert the augmented matrix to reduced row echelon form. This involves a series of row operations to make the matrix have a form where the leading coefficient (the first non-zero number from the left, also called the pivot) of each row is 1, and it is the only non-zero entry in its column.

Step 3 ：The reduced row echelon form of the matrix is \[\begin{array}{cccc}1 & 0 & 6 & 2 \\0 & 1 & 5 & 2 \\0 & 0 & 0 & 0\end{array}\]. This corresponds to the system of equations \(x + 6z = 2\), \(y + 5z = 2\), and \(0 = 0\). The third equation is always true, so it doesn't give us any new information.

Step 4 ：The first two equations tell us that \(x = 2 - 6z\) and \(y = 2 - 5z\). Since the problem asks us to set \(z = t\) if there is a free variable, we can substitute \(z = t\) into these equations to get \(x = 2 - 6t\) and \(y = 2 - 5t\).

Step 5 ：Final Answer: The solution for \(y\) is \(\boxed{2 - 5t}\).