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.