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.

Solve the system of equations \( x+y=7;x-y=1 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}x+y=7\\x-y=1\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=7-y\\x-y=1\end{array}\right.\) - step2: Substitute the value of \(x:\) \(7-y-y=1\) - step3: Subtract the terms: \(7-2y=1\) - step4: Move the constant to the right side: \(-2y=1-7\) - step5: Subtract the numbers: \(-2y=-6\) - step6: Change the signs: \(2y=6\) - step7: Divide both sides: \(\frac{2y}{2}=\frac{6}{2}\) - step8: Divide the numbers: \(y=3\) - step9: Substitute the value of \(y:\) \(x=7-3\) - step10: Calculate: \(x=4\) - step11: Calculate: \(\left\{ \begin{array}{l}x=4\\y=3\end{array}\right.\) - step12: Check the solution: \(\left\{ \begin{array}{l}x=4\\y=3\end{array}\right.\) - step13: Rewrite: \(\left(x,y\right) = \left(4,3\right)\) The solution to the system of equations \(x+y=7\) and \(x-y=1\) is \(x=4\) and \(y=3\). Therefore, the solution set is \((4,3)\).