# How can i solve these two equations simultaneously for A and B ?

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Asif Arshid on 26 Aug 2016
Edited: Asif Arshid on 27 Aug 2016
I have a system of 16 equations with 4 integration constants (A, B, C and D) in each soil layer (4 layers) and each soil layer has 4 stress-strain equations. I need to solve them simultaneously for 16 constants.
Below is the simplified form of two equations, which i am trying to solve for A and B.
int(5*besselj(0,x)*besselj(1, 0.5*x)*x*(A+5) ,x,0,10) = 0;
int(5*besselj(0,x)*besselj(1, 0.8*x)*x*(A+B) ,x,0,10) = A;

Walter Roberson on 27 Aug 2016
The multiply by (A+5) in the first equation leads to the trivial solution A=-5, zeroing the effect of the besselj .
You can substitute A into the second equation and then do a numeric solve, restriction your range for B from 5 onwards; the numeric solution turns out to be about B = 5.57463755753316
Asif Arshid on 27 Aug 2016
Edited: Asif Arshid on 27 Aug 2016
Thank you Walter Roberson for your quick reply. During my hit and trials of different functions, I got "vpasolve", it helped to solve for the equations upto the precision i was looking for.
z1 = int(5*besselj(0,x)*besselj(1,0.8*x)*x*(A+5),x,0,10);
z2 = int(5*besselj(0,x)*besselj(1,0.7*x)*x*(A+B),x,0,10);
[A, B] = vpasolve([z1==0, z2==A], [A, B])
One can equate z1 and z2 to any constant, variable or even functions of A and B, it will give you the approximate solution with reasonable precision. Thanks a lot again.