MATLAB: Using “solve” function to solve a system of equations in terms of two of 12 variables

MATLABsolvestructures

I am trying to solve these variables in terms of dQ3 and dQ5. (This is for structures homework, so we're dealing with virtual forces that will cancel in the end.) I am going to do it by hand, but I am still curious if there is a way to solve this in Matlab.
I looked at others' questions on Answers, but I only found examples of rearranging one equation instead of 10 simultaneously. dQ3 and dQ5 do not appear in all equations, so I am unsure how to specify that I want the solution in terms of these equations. Is this possible? Will it not work because the variables all have solutions that are 0?
clc;clear;
%VIRTUAL
syms dY1 dX1 dY3 dQ3 dQ5 dP12 dP14 dP23 dP24 dP25 dP35 dP45
eq1_v = 1.155*dY1 + dP14 == 0;
eq2_v = dX1 + dP12 + 0.5*dP14 == 0;
eq3_v = dP24 + dP25 == 0;
eq4_v = dP23 + 0.5*dP25 - dP12 - 0.5*dP24 == 0;
eq5_v = dY3 + 0.866*dP35 == 0;
eq6_v = dQ3 - 0.5*dP35 - dP23 == 0;
eq7_v = dP24 + dP14 == 0;
eq8_v = dP45 + 0.5*dP24 - 0.5*dP14 == 0;
eq9_v = dQ5 - dP25 - dP35 == 0;
eq10_v = dP35 - dP25 - 2*dP45 == 0;
eqs_v = [eq1_v eq2_v eq3_v eq4_v eq5_v eq6_v eq7_v eq8_v eq9_v eq10_v];
Sv = solve(eqs_v, [dY1, dX1, dY3, dP12, dP14, dP23, dP24, dP25,...
    dP35, dP45], 'dQ3', 'dQ5');
Sv.dY1
Sv.dX1
Sv.dY3
Sv.dP12
Sv.dP14
Sv.dP23
Sv.dP24
Sv.dP25
Sv.dP35
Sv.dP45
This is just another side question; just wondering if I can be lazy:
Also, is this the neatest way to display the variables and their numerical solutions (simply outputting 'Sv.–')? Is there a way to make a table? I figured out how to sort the numerical answers into a matrix, but I can't find how to turn the variables into strings without rewriting an entire new matrix of strings. I used the "fieldnames" function to get the variable names from the solve structure, but it outputs a cell array of cell arrays. Is there a shortcut?

Best Answer

arrayfun(@(EE) ismember(dQ3, symvar(EE)), eqs_v)
that will tell you which equations contain the first variable . Pick one of them . solve that one for the first variable . subs() the result for the variable in all of the other equations, leaving you with one fewer active equations .
repeat with respect to the second variable .
now back substitute the solution to the second equation into the solution to the first. You now have solutions for two variables and N-2 transformed equations .
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