SOLUTION: Solve the following system of equations and state answer in coordinate pairs?x^(2)+y^(2)=15 and x^(2)+y=-15 answers...(21,6)(10,-5),(21,-6)(-10,-5),(21,6)(-10,-5), no solution

Question 441886: Solve the following system of equations and state answer in coordinate pairs?x^(2)+y^(2)=15 and x^(2)+y=-15
answers...(21,6)(10,-5),(21,-6)(-10,-5),(21,6)(-10,-5), no solution
Found 2 solutions by htmentor, rwm:
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
[1]
[2]
Subtract equation 2 from equation 1:

Use the quadratic formula to solve for y:

This gives
y = -5,6
If we use equation [2] to find x, we see that no solution exists for either value of y:
y=-5:
y=6:
So there is no solution.
This can also be seen by the graphs of the two functions. Notice there are no points of intersection:

Answer by rwm(914) (Show Source): You can put this solution on YOUR website!
the first equation is a circle centered at the origin (0,0) radius sqrt(15) which is slightly less than 4
the second is a parabola with its vertex at y=-15
the two equations never cross so all solutions are complex.

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