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)

Question

asked Jun 18, 2020 165k views

1 Answer

HBomb · Answer 1 · 2020-06-23T01:39:43+0000

Answer:

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.