For which value(s) of kkk does the system {x2+y2=25x+y=k\begin{cases} x^2 + y^2 = 25 \\ x + y = k \end{cases}{x2+y2=25x+y=k have exactly one real solution?
k=5k = 5k=5 only
k=−5k = -5k=−5 only
k=5k = 5k=5 or k=−5k = -5k=−5
k=52k = 5\sqrt{2}k=52 or k=−52k = -5\sqrt{2}k=−52