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Serhud [2]
3 years ago
15

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

Mathematics
1 answer:
swat323 years ago
5 0

There are infinitely many solutions.

Algebraically, we can eliminate z 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.

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using a graph tool

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