How to solve this system of equal: x+y+z=1;x^2+y^2+z^2=1

Question

asked Jan 22, 2020 69.5k views

1 Answer

Dhavalcengg · Answer 1 · 2020-01-27T17:23:35+0000

There are infinitely many solutions.

Algebraically, we can eliminate
and try to solve for
x,y :

$x+y+z=1\implies z=1-x-y$

Then

x^2+y^2+(1-x-y)^2=1

$\implies x^2+y^2+1-2x+x^2-2y+y^2+2xy=1$

$\implies x^2-x+y^2-y+xy=0$

which is the equation of an ellipse.