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

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Question 1129199: Solve the system of equations:
Y=2x^2+3
Y=x+2
Enter one point as (x,y)
Enter two points as (x,y),(x,y)
Enter"no solution" as DNE.
Found 3 solutions by josgarithmetic, MathTherapy, ikleyn:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!


AMP Parsing Error of []: Invalid expression '': syntax error at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 203. .








from given;

OR



points:
( , ) , ( , )
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Solve the system of equations:
Y=2x^2+3
Y=x+2
Enter one point as (x,y)
Enter two points as (x,y),(x,y)
Enter"no solution" as DNE.
There are solutions, but these are NOT THEY! 



















points: ( -1/2, 3/2 ), ( 1, 3 )



So, AGAIN, wait for someone who knows what they're doing to give you sensible, correct answers.

HINT: Correct answers are NON-REAL (IMAGINARY). 

Answer by ikleyn(52788)   (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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