Question

Use the elimination method to solve the linear-quadratic system y=x^2+10, y=−7x−2.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the system using the elimination method, we need to eliminate one variable. Since the y term in the second equation is already isolated, we can substitute it into the first equation:

x^2 + 10 = -7x - 2

Now, we have a quadratic equation. To solve it, we can move all terms to one side:

x^2 + 7x + 12 = 0

This equation can be factored as:

(x + 3)(x + 4) = 0

Setting each factor equal to zero, we get:

x + 3 = 0 or x + 4 = 0

Solving these equations, we find:

x = -3 or x = -4

Now, we substitute these values back into either of the original equations to find the corresponding y values.

For x = -3:
y = (-3)^2 + 10
y = 9 + 10
y = 19

For x = -4:
y = (-4)^2 + 10
y = 16 + 10
y = 26

Therefore, the solutions to the system are (-3, 19) and (-4, 26).