Question

Use the elimination method to solve the linear-quadratic system y = x^2 -2x -2, y = 2x - 6.

A. (2, -2)
B. (-2, -2) and (-2, 2)
C. (2, -2) and (-2, 2)
D. (-2, -10)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the linear-quadratic system using the elimination method, we need to eliminate one of the variables. Let's eliminate the y variable by setting the two y-values equal to each other:

x^2 - 2x - 2 = 2x - 6

Next, let's simplify the equation:

x^2 - 2x - 2x + 2 = 2x - 2x - 6

x^2 - 4x + 2 = -6

Now, let's rewrite the quadratic equation in standard form:

x^2 - 4x + 8 = 0

We can solve this quadratic equation by factoring or by using the quadratic formula. However, upon closer inspection, the quadratic equation does not have real solutions. Therefore, there are no intersection points between the two curves, and the linear-quadratic system has no solution.

So the correct answer is: None of the above (There is no solution to the system).