\( x+y=k \) \( x-y=k \) The solution to the system shown is \( (2,2) \) \( (0, k) \) \( (k, 0) \)

To solve the system of equations, start by adding the two equations together: 1. \( x + y = k \) 2. \( x - y = k \) When you add them, the \( y \) terms cancel out: \( 2x = 2k \) which simplifies to \( x = k \). Next, substitute \( x = k \) into one of the original equations to find \( y \): Using \( x + y = k \): \( k + y = k \) therefore, \( y = 0 \). So the solution to the system is \( (k, 0) \).