Consider this system of equations:
y = x^2

y = x + k

for which value of k does the system have no real number solutions?
a.-2
b.0
c.2
d.4

for which value of k does the system have one real number solution?
a.-4
b.-2
c.-0.25
d.2

for which value of k does the system have two real number solutions?
a.-4
b.-2
c.-1
d.2

"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.