\( x+y=7 \) and \( x-y=1 \)

To solve the system of equations \( x+y=7 \) and \( x-y=1 \), you can use the method of elimination or substitution. Adding both equations together, \( (x+y) + (x-y) = 7 + 1 \) simplifies to \( 2x = 8 \), giving us \( x = 4 \). Now, substituting \( x = 4 \) back into the first equation, \( 4 + y = 7 \), leads to \( y = 3 \). So, \( x = 4 \) and \( y = 3 \)! Now, if you're wondering how to check your work, plug the values back into the original equations: for \( x+y=7 \), indeed \( 4+3=7 \), and for \( x-y=1 \), \( 4-3=1 \). Both equations hold true, confirming that \( (x, y) = (4, 3) \) is the right solution!