Use the elimination method to solve the linear-quadratic system y=x2−2x−2 , y=2x−6 .(1 point) Responses
(2,−2)
(−2,−2) and (−2,2)
(2,−2) and (−2,2)
(−2,−10)
To solve the system of equations using the elimination method, we need to eliminate one variable by manipulating the equations.
First, let's rearrange the second equation to isolate one of the variables:
y = 2x - 6
Now, we can substitute this expression for y into the first equation:
x^2 - 2x - 2 = 2x - 6
Next, let's simplify this equation:
x^2 - 4x + 4 = 0
This equation can be factored as:
(x - 2)^2 = 0
By taking the square root of both sides, we find that:
x - 2 = 0
x = 2
Substituting x = 2 back into the second equation, we can solve for y:
y = 2(2) - 6
y = 4 - 6
y = -2
Therefore, the solution to the system of equations is (2, -2).