38.5k views
5 votes
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

User Dionna
by
8.2k points

2 Answers

5 votes

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.

User Nischtname
by
8.5k points
6 votes

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

User Tomas Walek
by
7.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories