Question

Solve the system of equations. y = 2x y = x 2 – 15

A. (–3, –6) and (–5, –10)

B. (3, 6) and (–5, –10)

C. (3, 6) and (5, 10)

D. (–3, –6) and (5, 10)

Answer 1

D. (–3, –6) and (5, 10)

Explanation:

The system has equations:

`y=2x`...(1)

and

`y=x^2-15`...(2)

Equate both equations;

`x^2-15=2x`

Rewrite in standard form:

`x^2-2x-15=0`

We factor to obtain:

`(x+3)(x-5)=0`

By the zero product principle;

`(x+3)=0,(x-5)=0`

`\implies x=-3,x=5`

When x=-3, y=2(-3)=-6

This yields the ordered pair (-3,-6).

When x=5, y=2(5)=10

This yields the ordered pair (5,10).

The correct choice is D.