Question

Solve the following system: y=−x²−5x−1 and y=−2x+5.

a) (3,2)
b) (−3,2)
c) (3,−2)
d) (−3,−2)

Answer 1

After setting up the two equations y = -x² - 5x - 1 and y = -2x + 5 equal to each other and simplifying, it is clear that the resulting quadratic equation has no real solutions due to a negative discriminant. Therefore, none of the given options a), b), c), and d) are correct.

Step-by-step explanation:

To solve the system of equations y = -x² - 5x - 1 and y = -2x + 5, we set the two expressions for y equal to each other to find the possible values of x:

-x² - 5x - 1 = -2x + 5

Now, we bring all terms to one side to set up the equation for factoring or using the quadratic formula:

-x² - 5x - 1 + 2x - 5 = 0

-x² - 3x - 6 = 0

Using the quadratic formula, we have:

x = [-(-3) ± √((-3)² - 4(-1)(-6))] / (2(-1))

x = (3 ± √(9 - 24)) / -2

Since the discriminant (9 - 24) is negative, there are no real solutions to this equation. Hence, the given options a), b), c), and d) do not provide a correct solution, implying that there might have been a typo or error in typing the original equations.