"For which value of k does the system have no real number solutions?" The answer is 4, because 4+4≠16. "For which value of k does the system have one real number solution?" The answer is -0.25, because the linear line because tangent with the parent function.
"For which value of k does the system have two real number solutions?" The answer is 2, because the linear function intercepts the parent function 2 times.
- i hope these are the answers you are looking for.