What are the solutions of the system of equations for x + y = 2 and y = - 1/4 x^2 + 3

Use substitution

from first equation: y = 2 - x

Substitute in the 2nd equation:-

2 - x = - 1/4x^2 + 3

-1/4 x^2 + x + 1 = 0

solving this gives x = - 0.83, 4.83

Giving y = 2 - - 0.83 = 2.83, 2 - 4.83 = - 2.83

Answer (-0.83, 2.83) and (4.83, - 2.83)