Question

What are the solutions to the following system?

Answer 1

`\bf \begin{cases} -2x^2+y=-5\\ \boxed{y}=-3x^2+5\\ ----------\\ -2x^2+\left( \boxed{-3x^2+5} \right)=-5 \end{cases} \\\\\\ -5x^2+5=-5\implies -5(x^2-1)=-5\implies x^2-1=\cfrac{-5}{-5} \\\\\\ x^2-1=1\implies x^2=2\implies x=\pm√(2)`

and since we know what "x" is, then let's substitute it on say the 1st equation


`\bf -2x^2+y=-5\implies -2\left( \pm √(2) \right)^2+y=-5\implies -4+y=-5 \\\\\\ y=-1\\\\ -------------------------------\\\\ \left( √(2)~,~-1 \right)\qquad \left( -√(2)~,~-1 \right)`

Answer 2

C

Explanation: