Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
-$$\begin{array} { l }
x ^ { 2 } + y ^ { 2 } = 90 \
x ^ { 2 } - y ^ { 2 } = 72
\end{array}$$
A) $\{ ( 9,3 ) , ( 3,9 ) , ( - 9 , - 3 ) , ( - 3 , - 9 ) \}$
B) $\{ ( 9 , - 3 ) , ( 9,3 ) \}$
C) $\{ ( - 9 , - 3 ) , ( - 3 , - 9 ) \}$
D) $\{ ( 9,3 ) , ( - 9,3 ) , ( 9 , - 3 ) , ( - 9 , - 3 ) \}$

Question

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 90 \
x ^ { 2 } - y ^ { 2 } = 72
\end{array}$$
A) $\{ ( 9,3 ) , ( 3,9 ) , ( - 9 , - 3 ) , ( - 3 , - 9 ) \}$
B) $\{ ( 9 , - 3 ) , ( 9,3 ) \}$
C) $\{ ( - 9 , - 3 ) , ( - 3 , - 9 ) \}$
D) $\{ ( 9,3 ) , ( - 9,3 ) , ( 9 , - 3 ) , ( - 9 , - 3 ) \}$

Quizplus · Accepted Answer

To solve the system, add the two equations to eliminate $y^2$, resulting in $2x^2 = 162$, which simplifies to $x^2 = 81$. Thus, $x = \pm 9$. Substitute $x = 9$ and $x = -9$ into one of the original equations to find $y = \pm 3$. Therefore, the solutions are $(9,3)$, $(-9,3)$, $(9,-3)$, and $(-9,-3)$.

Give All Solutions of the Nonlinear System of Equations, Including x2+y2=90x2−y2=72\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 90 \\x ^ { 2 } - y ^ { 2 } = 72\end{array}x2+y2=90x2−y2=72​

Give All Solutions of the Nonlinear System of Equations, Including $\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 90 \\x ^ { 2 } - y ^ { 2 } = 72\end{array}$