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Two questions (1) Sollve and (2) Precision


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


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