Solve the system by the addition method. \[ \begin{array}{l}x+y=7 \\ x-y=1\end{array} \] Select the correct choice below and fill in any answer boxes present in your choice. The solution set is \{\}. (Simplify your answer. Type an ordered pair.) B. There are infinitely many solutions.

First, let's solve the system of equations using the addition method: 1. Start with the equations: \[ x + y = 7 \quad (1) \] \[ x - y = 1 \quad (2) \] 2. To eliminate \( y \), we can add both equations together: \[ (x + y) + (x - y) = 7 + 1 \] This simplifies to: \[ 2x = 8 \] Dividing by 2 gives: \[ x = 4 \] 3. Now, substitute \( x = 4 \) back into equation (1) to solve for \( y \): \[ 4 + y = 7 \] This gives: \[ y = 3 \] Thus, the solution set is \{(4, 3)\}.