Question

Which system is equivalent to y=-2x^2 ; y=x-2?

A) y=-2y^2-2; x=y-2

B) y=-2y^2+2; x=y+2

C) y=-2y^2-8y-8; x=y+2

D) y=-2y^2-8y-8; x=y-2

Answer 1

Option C -
`y=-2y^2-8y-8;\ x=y+2`

Explanation:

Given : The system of equation
`y=-2x^2\ ;y=x-2`

To find : Which system is equivalent to given system?

Solution :

Let Equation 1-
`y=-2x^2`

Equation 2 -
`y=x-2`

We can re-write equation 2 in terms of x as
`x=y+2`

Substitute the value of x in equation 1,

`y=-2(y+2)^2`

Solve,

`y=-2(y^2+2^2+2(y)(2))`

`y=-2(y^2+4+4y)`

`y=-2y^2-8-8y`

`y=-2y^2-8y-8`

The required equations are
`y=-2y^2-8y-8;\ x=y+2`

Therefore, option C is correct.

Answer 2

we are given

`y=-2x^2`

`y=x-2`

we can eliminate x from second equation

`x=y+2`

now, we can plug back in first equation

`y=-2(y+2)^2`

now, we can expand it

`y=-2(y^2+4y+4)`

`y=-2y^2-8y-8`

so, option-C.....................Answer