Solve the nonlinear system of equations.
-$$\left\{ \begin{array} { l }
x ^ { 2 } - y ^ { 2 } = 37 \
x ^ { 2 } + y ^ { 2 } = 43
\end{array} \right.$$
A) $( - 2 \sqrt { 10 } , - \sqrt { 3 } )$
B) $( 2 \sqrt { 10 } , \sqrt { 3 } ) , ( - 2 \sqrt { 10 } , \sqrt { 3 } ) , ( 2 \sqrt { 10 } , - \sqrt { 3 } ) , ( - 2 \sqrt { 10 } , - \sqrt { 3 } )$
C) $( 2 \sqrt { 10 } , \sqrt { 3 } ) , ( - 2 \sqrt { 10 } , \sqrt { 3 } )$
D) $\varnothing$

Question

Solve the nonlinear system of equations.
-$$\left\{ \begin{array} { l } 
x ^ { 2 } - y ^ { 2 } = 37 \
x ^ { 2 } + y ^ { 2 } = 43
\end{array} \right.$$
A) $( - 2 \sqrt { 10 } , - \sqrt { 3 } )$
B) $( 2 \sqrt { 10 } , \sqrt { 3 } ) , ( - 2 \sqrt { 10 } , \sqrt { 3 } ) , ( 2 \sqrt { 10 } , - \sqrt { 3 } ) , ( - 2 \sqrt { 10 } , - \sqrt { 3 } )$
C) $( 2 \sqrt { 10 } , \sqrt { 3 } ) , ( - 2 \sqrt { 10 } , \sqrt { 3 } )$
D) $\varnothing$

Quizplus · Accepted Answer

Adding the two equations gives $2x^2 = 80$, so $x^2 = 40$, and $x = \pm 2\sqrt{10}$. Substituting $x^2 = 40$ into either equation allows solving for $y^2$, leading to $y = \pm \sqrt{3}$. Thus, all combinations of $x$ and $y$ are solutions.

Solve the Nonlinear System of Equations {x2−y2=37x2+y2=43\left\{ \begin{array} { l } x ^ { 2 } - y ^ { 2 } = 37 \\x ^ { 2 } + y ^ { 2 } = 43\end{array} \right.{x2−y2=37x2+y2=43​

Solve the Nonlinear System of Equations $\left\{ \begin{array} { l } x ^ { 2 } - y ^ { 2 } = 37 \\x ^ { 2 } + y ^ { 2 } = 43\end{array} \right.$