Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
-$$\begin{array} { l }
2 x ^ { 2 } + x y + 2 y ^ { 2 } = 2 \
3 x ^ { 2 } - 5 x y + 3 y ^ { 2 } = 3
\end{array}$$
A) $\{ ( 1,0 ) , ( - 1,0 ) , ( 0,1 ) , ( 0 , - 1 ) \}$
B) $\{ ( 1,0 ) , ( 0,1 ) \}$
C) $\{ ( 1,0 ) \}$
D) $\{ ( 1,0 ) , ( - 1,0 ) \}$

Question

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
-$$\begin{array} { l } 
2 x ^ { 2 } + x y + 2 y ^ { 2 } = 2 \
3 x ^ { 2 } - 5 x y + 3 y ^ { 2 } = 3
\end{array}$$
A) $\{ ( 1,0 ) , ( - 1,0 ) , ( 0,1 ) , ( 0 , - 1 ) \}$
B) $\{ ( 1,0 ) , ( 0,1 ) \}$
C) $\{ ( 1,0 ) \}$
D) $\{ ( 1,0 ) , ( - 1,0 ) \}$

Quizplus · Accepted Answer

The solutions to the system of equations are $(1,0)$, $(-1,0)$, $(0,1)$, and $(0,-1)$.

Give All Solutions of the Nonlinear System of Equations, Including 2x2+xy+2y2=23x2−5xy+3y2=3\begin{array} { l } 2 x ^ { 2 } + x y + 2 y ^ { 2 } = 2 \\3 x ^ { 2 } - 5 x y + 3 y ^ { 2 } = 3\end{array}2x2+xy+2y2=23x2−5xy+3y2=3​

Give All Solutions of the Nonlinear System of Equations, Including $\begin{array} { l } 2 x ^ { 2 } + x y + 2 y ^ { 2 } = 2 \\3 x ^ { 2 } - 5 x y + 3 y ^ { 2 } = 3\end{array}$