Answer:
C)[tex](\sqrt{2}, -1 ) \text{and } (-\sqrt{2}, -1 )[/tex]
Step-by-step explanation:
Given system of equations:
[tex]$\left \{ {{-2x^2+y=-5} \atop {y=-3x^2+5}} \right. $[/tex]
[tex]$\left \{ {{y=-5+2x^2} \atop {y=-3x^2+5}} \right. $[/tex]
So,
[tex]-3x^2+5 = -5+2x^2[/tex]
[tex]-3x^2=2x^2-10[/tex]
[tex]-5x^2=-10[/tex]
[tex]x^2=2[/tex]
[tex]x_{1}=\sqrt{2}\\x_{2}=-\sqrt{2}[/tex]
[tex]y=-3(\sqrt{2} )^2+5[/tex]
[tex]y=-3(2)+5[/tex]
[tex]y=-6+5[/tex]
[tex]y=-1[/tex]
