\begin{tabular}{|l|l|}
\hline & The system has no solution. \\
System A & The system has a unique solution: \\
& $(x, y)=(\square, \square)$ \\
$2 x+y=6$ & The system has infinitely many solutions. \\
$-2 x=y-6$ & They must satisfy the following equation: \\
$y=\square$
\end{tabular}

Step 1 ：\(2x + y = 6\)

Step 2 ：\(-2x + 6 = y\)

Step 3 ：\(2x + y = -2x + 6\)

Step 4 ：\(4x = 6 - y\)

Step 5 ：\(x = \frac{6 - y}{4}\)

Step 6 ：\(2\left(\frac{6 - y}{4}\right) + y = 6\)

Step 7 ：\(\frac{6 - y}{2} + y = 6\)

Step 8 ：\(3 - \frac{y}{2} + y = 6\)

Step 9 ：\(3 + \frac{y}{2} = 6\)

Step 10 ：\(\frac{y}{2} = 3\)

Step 11 ：\(y = 6\)

Step 12 ：\(x = \frac{6 - 6}{4}\)

Step 13 ：\(x = 0\)

Step 14 ：\(2(0) + 6 = 6\)

Step 15 ：\(-2(0) = 6 - 6\)

Step 16 ：\(\boxed{(x, y) = (0, 6)}\)