Question

What are the solutions of the following system? -2x^2 + y=-5 y=-3x^2+5

Answer 1

Answer:

c

Step-by-step explanation:

Answer 2

$\begin{cases}-2x^2+y=-5\\y=-3x^2+5\end{cases}\\\\\\ -2x^2+(-3x^2+5)=-5\\\\ -2x^2-3x^2+5=-5\quad|-5\\\\-5x^2=-10\quad|:(-5)\\\\x^2=2\\\\ \boxed{x=-\sqrt{2}\qquad\vee\qquad x=\sqrt{2}}\\\\\\ y=-3x^2+5\qquad\vee\qquad y=-3x^2+5\\\\ y=-3(-\sqrt{2})^2+5\qquad\vee\qquad y=-3(\sqrt{2})^2+5\\\\ y=-3\cdot2+5\qquad\vee\qquad y=-3\cdot 2+5\\\\ y=-6+5\qquad\vee\qquad y=-6+5\\\\ \boxed{y=-1\qquad\vee\qquad y=-1}\\\\\\ \begin{cases}x=-\sqrt{2}\\y=-1\end{cases}\qquad\vee\qquad\begin{cases}x=\sqrt{2}\\y=-1\end{cases}$

Answer C.