Pts of Intersection, Circle and Line

Having some trouble breaking down this question in my worksheet; Find the intersection points of the line x+y=0 and the circle x^2+y^2=9.

Any guidance with the solution would be appreciated.

from x + y = 0 u get y = - x

use this relation in the circle's eqn u get :

x^2 + (-x)^2 = 9

=> 2 x^2 = 9 => x^2 = 9/2

hence x = +/- 3 / sqrt(2) , => y = - /+ 3 / sqrt(2)

so the 2 pts of intersection are : ( 3 / sqrt(2) , - 3 / sqrt(2)) , (- 3 / sqrt(2) , 3 / sqrt(2))

the line is y = - x which has slope of -1
the radius of the circle is 3
the intersections are 3( -1/sqrt(2) , 1/sqrt(2) ) and
3 (1/sqrt(2) , -1/sqrt(2) )
while the preceding answer is true, the math would lead you to believe there could be FOUR
possible results - you need to visualize the slope of the line to pick the right TWO out of the FOUR