Two questions (1) Sollve and (2) Precision

*To*: mathgroup at smc.vnet.net*Subject*: [mg67035] Two questions (1) Sollve and (2) Precision*From*: "Bharat Bhole" <bbhole at gmail.com>*Date*: Wed, 7 Jun 2006 05:10:24 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Would appreciate if someone can point out why Mathematica is not giving the expected output in the followng two cases. (1) I was trying to solve the follwing two linear equations using 'Solve'. *In: Solve[{64919121*x-159018721*y=8A1,41869520.5*x-102558961*y=8A0},{x,y}]* *Out: {}* However, the solution exists and is given by x = 205117922, y = 83739041 Why is Mathematica unable to solve this simple linear equation? Am I doing something wrong? (2) I suppose that the default precision for numerical calculations is MachinePrecision which is less than 16. If I increase the precision, should I not get more accurate results? The example below seems to contradict that. (i) Exact Calculation *In[1]: 123456789123 * 123456789123* *Out[1]: 15241578780560891109129* (ii) Numerical Calculation with Default Precision *In[2]: 123456789123 * 123456789123.0* *Out[2]: 1.52416 =D7 10^22* (iii) Numerical Calcuation with a higher precision. *In[3]:SetPrecision[ 123456789123 * 123456789123.0 , 50 ]* *Out[3]: 1.5241578780560891838464000000000000000000000000000 x 10^22* Now if I calculate Out[1]-Out[2], I get zero. But if I calculate Out[1]-Out[3], I get -729335.000000000000000000000000000

**Follow-Ups**:**Re: Two questions (1) Sollve and (2) Precision***From:*"Chris Chiasson" <chris@chiasson.name>