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Equations system with zero


Hi alll,

Let the following equations system for x, y Reals

Solve[{y/(9y)==0/(5x),x^2+3y^2},{x,y}]
{}

Mathematica 6.0.1 yields no solution. But the solutions exist. They
are four solutions

x=0, y=+-Sqrt[1/3]
y=0, x=+-1

Mathematica first simplifying y/(9y) -> 1/9 and it compare with 0/(5x) -
> and yiels False and it stops the process. Is this correct?.

In my opinion, the correct process would be
(5*x*y)==(9*y*0)
5xy=0 ----> x=0 or y=0

and substitution in the second equation.


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