Equations system with zero

*To*: mathgroup at smc.vnet.net*Subject*: [mg91360] Equations system with zero*From*: Miguel <mibelair at hotmail.com>*Date*: Mon, 18 Aug 2008 03:36:41 -0400 (EDT)

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.