Question

Solve the system of equations given as

x^2 +y^2 =16
y-4 = -x^2

Answer 1

We have x^2=4-y , from the second equation.So we replace it to the first one :
4-y+y^2=16 @Romwil

Answer 2

well you have a circle with a centre at the origin and readius 4

and a concave down parabola with a vertex at (0, 4)

Answer 3

so there are 3 points of intersection...

Answer 4

Refer to the attachment generated with the Mathematica 9 program.

Answer 5

props to him ^^ he has taken the time to graphically solve it with a calculator, rather than completely algebraically :)