SOLUTION: (8) Question: How many solutions does this nonlinear system have? 2y=2x^2+4x+9 y=x^2+2x+3 (A) 0 (B) 1 (C) 2 (D) 3 (E) Infinite solutions Thanks! PLEASE NOTE THIS IS T

Question 30458: (8) Question:
How many solutions does this nonlinear system have?
2y=2x^2+4x+9
y=x^2+2x+3
(A) 0
(B) 1
(C) 2
(D) 3
(E) Infinite solutions
Thanks!
PLEASE NOTE THIS IS THE CORRECT QUESTION AND WRITTEN EXACTLY HOW IT IS FOUND IN MY WORK ~
Answer by Fermat(136) (Show Source): You can put this solution on YOUR website!
There are no solutions!
Your two eqns are,
2y=2x^2+4x+9
y=x^2+2x+3
Dividing the top eqn by 2, the system of eqns becomes,
y=x^2+2x+4.5
y=x^2+2x+3
These are two "parallel" curves (parabolas).
One parabola cuts the y-axis at y = 4.5.
The other parabola cuts the y-axis at y = 3.
The two parabolas are the same size/shape and will never intersect, hence no solutions.

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