Question 602806
x2 + y2 = 4
x2 + y = 40 
------------ Subtract
y^2 - y = -36
{{{y^2 - y + 36 = 0}}}
{{{y = 1/2 +- i*sqrt(143)/2}}}
------------
{{{x^2 = 40 - y = 39.5 +- i*sqrt(143)/2}}}
{{{x = sqrt(39.5 +- i*sqrt(143)/2)}}}
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If you graph these, you'll see a circle and a parabola, and no intersections.
--> no real solutions.
Further manipulation is possible, but I'm not gonna do a lot of work and then have you say you made a typo.