Question 1129199
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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[1,2]}}} = {{{(1 +- sqrt(-7))/(2*2)}}} = {{{(1 +- i*sqrt(7))/4}}}.


<U>Answer</U>.  This system HAS NO real solution/solutions.

         It has two distinct solution in complex numbers  (x,y) = ({{{(1 + i*sqrt(7))/4}}},{{{(1 + i*sqrt(7))/4 +2}}}}  and  (x,y) = ({{{(1 - i*sqrt(7))/4}}},{{{(1 - i*sqrt(7))/4 +2}}}).
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Solved and explained.


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