How to solve a system of equations for specific variables in terms of specific variables?

let's say I have a system of n number of equations containing m number of variables, and I want to solve these equations for specific h number of variables in terms of specific u variables, given the fact that this operation is possible and we do not want to do it by hand, is it this possible?

for example I have 7 equations:

syms vi r1 is vc r2 ix vL v1 r2 r3 ir ii d1 d2
eq1 = -vi+3*is+vc+15*ix==0
eq2 = vL+4*v1-15*ix-vc==0
eq3 = -4*v1+6*ir==0
eq4 = is==ix+ii
eq5 = vi-v1==3*is
eq6 = ix==0.15*d1
eq7 = vL==0.375*d2

And I want to solve for 'd1' and 'd2' and 'ir' in terms of 'vc' and 'ii' and 'vi' GIVEN THE FACT THAT THIS OPERATION IS POSSIBLE, the output is:

d1 = (-0.37037)*vc + (-1.111111)*ii + (0.37037)*vc
d2 = (-1.33333)*vc + (20.000000)*ii + (-6.6666)*vc
ir = ( 0.11111)*vc + (-1.666666)*ii + (0.55555)*vc

Thanks!

Answer 1

[Walter Roberson]

syms vi r1 is vc r2 ix vL v1 r2 r3 ir ii d1 d2
eq1 = -vi+3*is+vc+15*ix==0

eq1 = 

eq2 = vL+4*v1-15*ix-vc==0

eq2 = 

eq3 = -4*v1+6*ir==0

eq3 = 

eq4 = is==ix+ii

eq4 = 

eq5 = vi-v1==3*is

eq5 = 

eq6 = ix==0.15*d1

eq6 = 

eq7 = vL==0.375*d2

eq7 = 

eqns = [eq1, eq2, eq3, eq4, eq5, eq6, eq7];
in_terms_of = [vc, vi, ii];
solve_for = setdiff(symvar(eqns), in_terms_of)

solve_for = 

sol = solve(eqns, solve_for)

sol = struct with fields:
    d1: [1×1 sym]
    d2: [1×1 sym]
    ir: [1×1 sym]
    is: [1×1 sym]
    ix: [1×1 sym]
    v1: [1×1 sym]
    vL: [1×1 sym]

subs([solve_for].', sol)

ans = 

[Mohamad Balawi]

You are truly amazing person, thank you very much, you have helped me a lot.

[Mohamad Balawi]

@Walter Roberson Sorry to bother you again, is there a way to show the constants in the final result in decimal format instead of fractions?

[Walter Roberson]

Ndigit = 5;
syms vi r1 is vc r2 ix vL v1 r2 r3 ir ii d1 d2
eq1 = -vi+3*is+vc+15*ix==0

eq1 = 

eq2 = vL+4*v1-15*ix-vc==0

eq2 = 

eq3 = -4*v1+6*ir==0

eq3 = 

eq4 = is==ix+ii

eq4 = 

eq5 = vi-v1==3*is

eq5 = 

eq6 = ix==0.15*d1

eq6 = 

eq7 = vL==0.375*d2

eq7 = 

eqns = [eq1, eq2, eq3, eq4, eq5, eq6, eq7];
in_terms_of = [vc, vi, ii];
solve_for = setdiff(symvar(eqns), in_terms_of)

solve_for = 

sol = solve(eqns, solve_for)

sol = struct with fields:
    d1: [1×1 sym]
    d2: [1×1 sym]
    ir: [1×1 sym]
    is: [1×1 sym]
    ix: [1×1 sym]
    v1: [1×1 sym]
    vL: [1×1 sym]

vpa(subs([solve_for].', sol), Ndigit)

ans = 

[Mohamad Balawi]

Thank you sir for your time and effort.