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.

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> 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.      Log On


   

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(39617) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E2%2B3=x%2B2
2x%5E2-x%2B1=0

x=%281%2B-+sqrt%281-4%2A2%29%29%2F4

x=%281%2B-+sqrt%28-7%29%29%2F4

x=%281%2B-+i%2Asqrt%287%29%29%2F4


y=x%2B2 from given;
y=%289-i%2Asqrt%287%29%29%2F4
OR
y=%289%2Bi%2Asqrt%287%29%29%2F4


points:
( %281-i%2Asqrt%287%29%29%2F4, %289-i%2Asqrt%287%29%29%2F4 ) , ( %281%2Bi%2Asqrt%287%29%29%2F4, %289%2Bi%2Asqrt%287%29%29%2F4 )

Answer by MathTherapy(10552) About Me  (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! 



2x%5E2%2B3=x%2B2

2x%5E2-x%2B1=0

cross%28%282x%2B1%29%28x-1%29=0%29





cross%28system%28x=-1%2F2%2Cor%2Cx=1%29%29





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(52787) About Me  (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. 


x%5B1%2C2%5D = %281+%2B-+sqrt%28-7%29%29%2F%282%2A2%29 = %281+%2B-+i%2Asqrt%287%29%29%2F4.


Answer.  This system HAS NO real solution/solutions.

         It has two distinct solution in complex numbers  (x,y) = (%281+%2B+i%2Asqrt%287%29%29%2F4,%281+%2B+i%2Asqrt%287%29%29%2F4+%2B2}  and  (x,y) = (%281+-+i%2Asqrt%287%29%29%2F4,%281+-+i%2Asqrt%287%29%29%2F4+%2B2).

Solved and explained.

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