Question 618497
x^2+y^2 +2x +2y =0

so using substitution method:

x^2 +y^2 = -2x -2y

(-2x -2y) -2x -2y = 0

-4x - 4y = 0

-4x = 4y

x = -y or y=-x

Sub y=-x in for either equation.

x^2 + (-x)^2 -2x + 2x = 0
2x^2 = 0

x = 0 <--------


x =-y

0 =-y
 
y=0   <------

If you want to visualize this, you have two circles that intersect at (0,0).