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

Question

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

Quizplus · Accepted Answer

Solving the system, we can express $y$ in terms of $x$ from the second equation: $y = -1 - x$. Substituting this into the first equation gives $x^2 + (-1 - x)^2 = 1$, which simplifies to $2x^2 + 2x = 0$, leading to $x(x + 1) = 0$. Thus, $x = 0$ or $x = -1$. Substituting these values back into $y = -1 - x$ gives the pairs $(0, -1)$ and $(-1, 0)$.

Give All Solutions of the Nonlinear System of Equations, Including x2+y2=1x+y=−1\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 1 \\x + y = - 1\end{array}x2+y2=1x+y=−1​

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