Find one pair of real numbers, $(x, y),$ such that $x + y = 6$ and $x^3 + y^3 = 144.$

For this case we have the following system of equations:
 x + y = 6
 x ^ 3 + y ^ 3 = 144
 Solving the system of equations graphically we have that one of the solutions is:
 x = 3-root (5)
 y = 3 + root (5)
 Then, an ordered pair that satisfies both equations:
 (x, y) = (3-root (5), 3 + root (5))
 
 (x, y) = (3-root (5), 3 + root (5))