Check all of the following that are solutions to the system shown below.
y = -x² - x + 2 and x + y = -2
(2, -4)
(-2, 4)
(-2, 0)
(0, -2)

From second equation y = -2-x

Plug this into the first equation:-

- 2 - x = -x^2 - x + 2

x^2 + x - 2 - 2 - x = 0

x^2 - 4 = 0

x^2 = 4

x + +/- 2

Plug these values into x + y = -2 :-
x = 2:- 
2 + y = -2   

so y = -4 

so one solution is (2,-4)

Now try x = -2

- 2 + y = -2

y = 0 

so the second solution is ( -2 , 0)

So A and C  are correct