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

Question

asked Apr 1, 2018 38.5k views

2 Answers

Nischtname · Answer 1 · 2018-04-04T03:31:47+0000

Answer:

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.

Tomas Walek · Answer 2 · 2018-04-07T09:56:22+0000

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