Question
Use the elimination method to solve the linear-quadratic system y=x2−2x−2 , y=2x−6 .(1 point) Responses (−2,−10) left parenthesis negative 2 comma negative 10 right parenthesis (−2,−2) and (−2,2) left parenthesis negative 2 comma negative 2 right parenthesis and left parenthesis negative 2 comma 2 right parenthesis (2,−2) and (−2,2) left parenthesis 2 comma negative 2 right parenthesis and left parenthesis negative 2 comma 2 right parenthesis (2,−2)
Answers
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GPT 3.5
First, we'll write the equations in standard form:
y = x^2 - 2x - 2
y = 2x - 6
To use the elimination method, we need to eliminate one of the variables. In this case, we can eliminate y by multiplying the second equation by -1:
-y = -2x + 6
Now we can add the two equations together:
(x^2 - 2x - 2) + (-2x + 6) = 0
Rearranging the terms, we get:
x^2 - 4x + 4 = 0
Now we can solve this quadratic equation by factoring or using the quadratic formula:
(x - 2)(x - 2) = 0
(x - 2)^2 = 0
x - 2 = 0
x = 2
Now we can substitute this value of x back into one of the original equations:
y = 2(2) - 6
y = 4 - 6
y = -2
Therefore, the solution to the system is (2, -2).
y = x^2 - 2x - 2
y = 2x - 6
To use the elimination method, we need to eliminate one of the variables. In this case, we can eliminate y by multiplying the second equation by -1:
-y = -2x + 6
Now we can add the two equations together:
(x^2 - 2x - 2) + (-2x + 6) = 0
Rearranging the terms, we get:
x^2 - 4x + 4 = 0
Now we can solve this quadratic equation by factoring or using the quadratic formula:
(x - 2)(x - 2) = 0
(x - 2)^2 = 0
x - 2 = 0
x = 2
Now we can substitute this value of x back into one of the original equations:
y = 2(2) - 6
y = 4 - 6
y = -2
Therefore, the solution to the system is (2, -2).