Question

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

Answer 1

"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. 

Answer 2

Answer:

For which value of k does the system have no real number solutions?  

✔ –2

For which value of k does the system have one real number solution?  

✔ –0.25

For which value of k does the system have two real number solutions?  

✔ 2