Question

What are the solutions to the following system?

{-2x^2+y=-5
y=-3x^2+5

A)(0, 2)
B) (1, –2)
C)(sq2.-1) and (-sq2.-1)
D)(sq5.-10) and (-sq5.-10)

Answer 1

C)
`(√(2), -1 ) \text{and } (-√(2), -1 )`

Explanation:

Given system of equations:

`$\left \{ {{-2x^2+y=-5} \atop {y=-3x^2+5}} \right. $`

`$\left \{ {{y=-5+2x^2} \atop {y=-3x^2+5}} \right. $`

So,

`-3x^2+5 = -5+2x^2`

`-3x^2=2x^2-10`

`-5x^2=-10`

`x^2=2`

`x_(1)=√(2)\\x_(2)=-√(2)`

`y=-3(√(2) )^2+5`

`y=-3(2)+5`

`y=-6+5`

`y=-1`