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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)

1 Answer

7 votes

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.

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