Use the Gauss-Jordan method to solve the following system of equations.
\[
\begin{array}{c}
x+y=8 \\
3 x+2 y=18
\end{array}
\]

Step 1 ：Represent the system of equations as an augmented matrix: \[\begin{array}{cc|c} 1 & 1 & 8 \\ 3 & 2 & 18 \end{array}\]

Step 2 ：Transform the matrix into a form where the leading coefficient of each row is 1, and all other numbers in the column containing the pivot are 0. The transformed matrix is: \[\begin{array}{cc|c} 1 & 1 & 8 \\ 0 & 1 & 6 \end{array}\]

Step 3 ：The first row of the matrix corresponds to the equation \(x + y = 8\), and the second row corresponds to the equation \(y = 6\). Therefore, the solution to the system of equations is \(x = 8 - y = 2\) and \(y = 6\).

Step 4 ：Final Answer: The solution to the system of equations is \(\boxed{x = 2}\) and \(\boxed{y = 6}\).