Question 441886
{{{x^2 + y^2 = 15}}} [1]
{{{x^2 + y = -15}}}  [2]
Subtract equation 2 from equation 1:
{{{y^2 - y = 30 -> y^2 - y - 30 = 0}}}
Use the quadratic formula to solve for y:
{{{y = (1 +- sqrt(1+120))/2}}}
This gives {{{y = (1 +- 11)/2}}}
y = -5,6
If we use equation [2] to find x, we see that no solution exists for either value of y:
y=-5: {{{x^2 - 5 = -15 -> x^2 < 0}}}
y=6:  {{{x^2 + 6 = -15 -> x^2 < 0}}}
So there is no solution.  
This can also be seen by the graphs of the two functions.  Notice there are no points of intersection:
{{{graph(400,400,-30,30,-30,30,sqrt(15-x^2),-sqrt(15-x^2),-15-x^2)}}}