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

To solve the system of equations, you can use substitution or elimination. Let’s go with the elimination method for some math magic! If you add the two equations, \( (x + y) + (x - y) = 7 + 1 \), you get \( 2x = 8 \). Dividing by 2, we find \( x = 4 \). Now, substitute \( x \) back into one of the original equations, like \( x + y = 7 \). Substitute \( 4 \) for \( x \), so \( 4 + y = 7 \), which gives \( y = 3 \). Voilà! The solution is \( x = 4 \) and \( y = 3 \). Let’s not forget about the fun in graphing! If you graph both equations on a coordinate plane, you’ll see two lines intersecting at the point \( (4, 3) \). This visual representation of their solution can be quite enlightening, as it reveals how these linear equations represent relationships in a geometric format. It’s like finding where two friends meet up after making different plans!