Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
-$$\begin{array} { l }
x ^ { 2 } + 3 x y + y ^ { 2 } = 4 \
x ^ { 2 } - 3 x y - y ^ { 2 } = 4
\end{array}$$
A) $\{ ( 0,2 ) , ( 0 , - 2 ) , ( 2 , - 6 ) , ( - 2,6 ) \}$
B) $\{ ( 2,0 ) , ( - 2,0 ) , ( 2 , - 6 ) , ( - 2,6 ) \}$
C) $\{ ( 2 , - 6 ) , ( - 2,6 ) \}$
D) $\{ ( 2,0 ) , ( - 2,0 ) \}$

Question

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
-$$\begin{array} { l } 
x ^ { 2 } + 3 x y + y ^ { 2 } = 4 \
x ^ { 2 } - 3 x y - y ^ { 2 } = 4
\end{array}$$
A) $\{ ( 0,2 ) , ( 0 , - 2 ) , ( 2 , - 6 ) , ( - 2,6 ) \}$
B) $\{ ( 2,0 ) , ( - 2,0 ) , ( 2 , - 6 ) , ( - 2,6 ) \}$
C) $\{ ( 2 , - 6 ) , ( - 2,6 ) \}$
D) $\{ ( 2,0 ) , ( - 2,0 ) \}$

Quizplus · Accepted Answer

The system of equations simplifies to two separate equations: $x^2 + y^2 = 4$ and $3xy = 0$. Solving these gives the solutions $(2,0)$, $(-2,0)$, $(2,-6)$, and $(-2,6)$.

Give All Solutions of the Nonlinear System of Equations, Including x2+3xy+y2=4x2−3xy−y2=4\begin{array} { l } x ^ { 2 } + 3 x y + y ^ { 2 } = 4 \\x ^ { 2 } - 3 x y - y ^ { 2 } = 4\end{array}x2+3xy+y2=4x2−3xy−y2=4​

Give All Solutions of the Nonlinear System of Equations, Including $\begin{array} { l } x ^ { 2 } + 3 x y + y ^ { 2 } = 4 \\x ^ { 2 } - 3 x y - y ^ { 2 } = 4\end{array}$