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

Answer 1

To solve the linear-quadratic system using the elimination method, we need to eliminate one variable (either x or y) by manipulating the equations.

Given the equations:
(1) y = x^2 - 2x - 2
(2) y = 2x - 6

Since both equations are already solved for y, we can set them equal to each other to eliminate y:

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

Rearranging the equation:

x^2 - 4x + 4 = 0

Now we have a quadratic equation, which we can solve by factoring or applying the quadratic formula. In this case, the quadratic equation factors as:

(x - 2)(x - 2) = 0

This leads to the solution:

x = 2

Substituting x = 2 into either one of the original equations, we find:

y = (2)^2 - 2(2) - 2
y = 4 - 4 - 2
y = -2

Therefore, the solution to the linear-quadratic system is (x, y) = (2, -2).