Give All Solutions of the Nonlinear System of Equations, Including $$\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 1 \\x + y = 1\end{array}$$

Multiple Choice

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
- $$\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 1 \\x + y = 1\end{array}$$

A) $\{ ( 1,0 ) , ( 0 , - 1 ) \}$
B) $\{ ( 1,0 ) , ( 0,1 ) \}$
C) $\{ ( - 1,0 ) , ( 0,1 ) \}$
D) $\{ ( - 1,0 ) , ( 0 , - 1 ) \}$