Answer:
The solutions of this system of equations are (-2, -2) and (1, 1).
Step-by-step explanation:
Let be the following system of equations:
[tex]y = -x^{2}+2[/tex] (1)
[tex]y = x[/tex] (2)
(2) in (1):
[tex]y = -y^{2}+2[/tex]
[tex]y^{2}+y-2 = 0[/tex]
This polynomial can be solved analytically by Quadratic Formula:
[tex]y_{1} = 1[/tex], [tex]y_{2} = -2[/tex]
Hence, the solutions of this system of equations are (-2, -2) and (1, 1).
