Answer:
[tex]y = - {x}^{2} - 2 - - - (i) \\ - x + y = - 4 - - - (ii)[/tex]
from equation (ii):
[tex]y = x - 4 - - - (iii)[/tex]
substitute y in (i) with y in (iii):
[tex] - {x}^{2} - 2 = x - 4 \\ - {x}^{2} - x + 2 = 0 \\ {x}^{2} + x - 2 = 0 \\ (x - 1)(x + 2) = 0 \\ \\ { \underline{x = 1 \: \: and \: \: - 2}}[/tex]
find y:
[tex]y = x - 4 \\ { \underline{y = - 3 \: \: and \: \: - 6}}[/tex]
therefore points of intersection:
[tex]{ \underline{ \underline{ \boxed{ \boxed{(1, \: - 3) \: \: and \: \: ( - 2, \: - 6)}}}}}[/tex]
