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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)

Respuesta :

kudzordzifrancis

Answer:

D. (–3, –6) and (5, 10)

Step-by-step explanation:

The system has equations:

[tex]y=2x[/tex]...(1)

and

[tex]y=x^2-15[/tex]...(2)

Equate both equations;

[tex]x^2-15=2x[/tex]

Rewrite in standard form:

[tex]x^2-2x-15=0[/tex]

We factor to obtain:

[tex](x+3)(x-5)=0[/tex]

By the zero product principle;

[tex](x+3)=0,(x-5)=0[/tex]

[tex]\implies x=-3,x=5[/tex]

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.