Solve the nonlinear system of equations.
-$$\left\{ \begin{aligned}
x ^ { 2 } - 3 y ^ { 2 } & = - 8 \
y & = x
\end{aligned} \right.$$
A) $( 2 , - 2 )$
B) $( 2,2 )$
C) $( 2 , - 2 ) , ( - 2,2 )$
D) $( 2,2 ) , ( - 2 , - 2 )$

Question

Quizplus · Accepted Answer

Substituting $y = x$ into the first equation gives $x^2 - 3x^2 = -8$, simplifying to $-2x^2 = -8$, which solves to $x^2 = 4$. Thus, $x = 2$ or $x = -2$, and since $y = x$, the solutions are $(2, 2)$ and $(-2, -2)$.

Solve the Nonlinear System of Equations {x2−3y2=−8y=x\left\{ \begin{aligned}x ^ { 2 } - 3 y ^ { 2 } & = - 8 \\y & = x\end{aligned} \right.{x2−3y2y​=−8=x​

Solve the Nonlinear System of Equations $\left\{ \begin{aligned}x ^ { 2 } - 3 y ^ { 2 } & = - 8 \\y & = x\end{aligned} \right.$