<h2>
Hello!</h2>
The answer is: B. (0,-4) and (2,0)
<h2>
Why?</h2>
We can solve the system of equations using the substitution method, meaning that we must substitute one equation into the other equation, resulting in a principal equation.
So,
We are given two equations:
![y=2x-4](https://tex.z-dn.net/?f=y%3D2x-4)
and,
![y=x^{2} -4](https://tex.z-dn.net/?f=y%3Dx%5E%7B2%7D%20-4)
So, making the equation equals, we have that:
![2x-4=x^{2}-4\\x^{2}-2x-4+4=0\\x^{2}-2x=0\\x(x-2)=0\\](https://tex.z-dn.net/?f=2x-4%3Dx%5E%7B2%7D-4%5C%5Cx%5E%7B2%7D-2x-4%2B4%3D0%5C%5Cx%5E%7B2%7D-2x%3D0%5C%5Cx%28x-2%29%3D0%5C%5C)
Finding where the function tends to 0 (roots), we have:
![x(x-2)=0\\x1=0\\x2=2](https://tex.z-dn.net/?f=x%28x-2%29%3D0%5C%5Cx1%3D0%5C%5Cx2%3D2)
Then, substituting each value of "x" in the first equation, we will find the correct options:
Substituting "x" equal to 0 into the first equation, we have:
![y=2(0)-4=-4](https://tex.z-dn.net/?f=y%3D2%280%29-4%3D-4)
So, the point will be (0,-4)
Substituting "x" equal to 2 into the first equation, we have:
![y=2(2)-4=4-4=0](https://tex.z-dn.net/?f=y%3D2%282%29-4%3D4-4%3D0)
So, the point will be (2,0)
Therefore, the correct option is B. (0,-4) and (2,0)
Have a nice day!