SOLUTION: Solve the system of equations: Y=2x2+3 Y=x+2 Enter one point as (x,y) Enter teo points as (x,y),(x,y) Enter"no solution" as DNE.

Question 1129198: Solve the system of equations:
Y=2x2+3
Y=x+2
Enter one point as (x,y)
Enter teo points as (x,y),(x,y)
Enter"no solution" as DNE.
Answer by ikleyn(52794) (Show Source): You can put this solution on YOUR website!
.

y = 2x^2 + 3
y = x + 2


Left sides are identical - hence, right sides are equal:


2x^2 + 3 = x + 2  ====>

2x^2 -x + 1 = 0.


The discriminant = b^2 - 4ac = (-1)^2 - 4*2*1 = 1 - 8 = -7  ====>


There is no real solution. 


 =  = .


Answer.  This system HAS NO real solution/solutions.

         It has two distinct solution in complex numbers  (x,y) = (,}  and  (x,y) = (,).

Solved and explained.

You can simplify these complex number solutions, if you need (if you need to have them, at all).

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