What are the solutions of the system?

{y=-6x-6
y=x^2-5x-6

answer choices:

a) (0, -1) and (0, -6)

b) (0, -1) and (-6, 0)

c) (-1, 0) and (-6, 0)

d) (-1, 0) and (0, -6)

D. (-1, 0) and (0, -6)

Step-by-step explanation:

The system of equations:

y = -6x - 6

y = x² - 5x - 6

We equate the two equations;

-6x - 6 = x² - 5x - 6

x² + x + 0 = 0

x² + x = 0

x(x + 1) = 0

So, x = 0 or -1

When x = 0,

Then y = -6(0) - 6 = -6

When x = -1,

Then y = -6(-1) - 6 = 6 - 6 = 0

So the answer is: (0, -6) and (-1, 0)

option 1: determine whether   (-x)^4 - (-x)^3 is equivalent to f(x)=x^4-x^3

step-by-step explanation:

first of all we will define the even function:

an even function is a function in which

f(-x) = f(x)

theoretically, putting -x in place of x gives the same original function.

so, for the given function:

f(x)=x^4-x^3

f(-x) = (-x)^4 - (-x)^3 should be equal to the original function f(x)=x^4-x^3

hence, option 1 is correct ..