Answer:
Option D.
Step-by-step explanation:
The given system of equations is
[tex]y=2x[/tex] ....(i)
[tex]y=x^2-15[/tex] ...(ii)
From (i) and (ii) we get
[tex]x^2-15=2x[/tex]
[tex]x^2-2x-15=0[/tex]
[tex]x^2-5x+3x-15=0[/tex]
[tex]x(x-5)+3(x-5)=0[/tex]
[tex](x-5)(x+3)=0[/tex]
Using zero produc property we get
[tex]x-5=0\Rightarrow x=5[/tex]
[tex]x+3=0\Rightarrow x=-3[/tex]
If x=5, then
[tex]y=2(5)=10[/tex]
If x=-3, then
[tex]y=2(-3)=-6[/tex]
The solutions of the given system of equations are (-3,-6) and (5,10).
Therefore, the correct option is D.
