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solve a system of equations symbolically with R2018a
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>> eqn1='(Fa0*x1)/0.1*(9.05*(1-x1))*(27.8-9.05*x1))==3785'
eqn1 =
'(Fa0*x1)/0.1*(9.05*(1-x1))*(27.8-9.05*x1))==3785'
>> eqn2='(Fa0*(x2-x1))/0.1*(9.05*(1-x2))*(27.8-9.05*x2))==3785'
eqn2 =
'(Fa0*(x2-x1))/0.1*(9.05*(1-x2))*(27.8-9.05*x2))==3785'
>> eqn3='(Fa0*(0.95-x2))/0.1*(9.05*(1-0.95))*(27.8-9.05*0.95))==3785'
eqn3 =
'(Fa0*(0.95-x2))/0.1*(9.05*(1-0.95))*(27.8-9.05*0.95))==3785'
>> solT=solve(eqn1,eqn2,eqn3,x1,x2,Fa0)
Error using solve>getEqns (line 418)
List of equations must not be empty.
Error in solve (line 226)
[eqns,vars,options] = getEqns(varargin{:});
Answers (1)
Walter Roberson
on 16 Jul 2019
You are using R2018b or later. solve() no longer accepts character vectors for equations.
Furthermore, each of your equations has an extra ) before the ==
5 Comments
Katy Skillings
on 16 Jul 2019
Great thank you so much. Do you have any suggestions on easily solving the three equations for the three unknowns?
Walter Roberson
on 17 Jul 2019
syms x1 x2 Fa0
eqn1=(Fa0*x1)/0.1*(9.05*(1-x1))*(27.8-9.05*x1)==3785
eqn2=(Fa0*(x2-x1))/0.1*(9.05*(1-x2))*(27.8-9.05*x2))==3785
eqn3=(Fa0*(0.95-x2))/0.1*(9.05*(1-0.95))*(27.8-9.05*0.95)==3785
solT=solve(eqn1,eqn2,eqn3,x1,x2,Fa0)
>> solT.x1
ans =
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Walter Roberson
on 17 Jul 2019
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(2813441280502164056685917619200458752000000000000000000000000000000*z^3)/2638299689840923267400928133978279323453268156704319 - (1047142599503041327543418476239519744000000000000000000000000000000000000*z^2)/20264779917668131616906528997087163483444552711645874239 - (129725245369116609526016420075945328640000000000000000000000000000000000000000*z)/155653774547608918949459049226626502716337609378151960029759 - 5609740340286123655179088435716554752000000000000000000000000000000000000000000000/1195576642300184106450794957109718167364189177633585204988578879, z, 9)^6)/63142993704454431891783680000000000000000000000000000000 + (703558362212137899332129394101759976766459179357552489*root(z^9 + (876723486400000*z^8)/202893300079 + (12991106484046625280000000000*z^7)/2166615327207744284539 + (76083178071679839453913088000000000000000*z^6)/23136407038890612331350973009399 + (150940543804112324360187616985088000000000000000000000*z^5)/247064314531132675315834249803401104970659 + (4108029355821456200801735089921720320000000000000000000000000*z^4)/343483880984367044317267039965926223597613351999 - (2813441280502164056685917619200458752000000000000000000000000000000*z^3)/2638299689840923267400928133978279323453268156704319 - (1047142599503041327543418476239519744000000000000000000000000000000000000*z^2)/20264779917668131616906528997087163483444552711645874239 - (129725245369116609526016420075945328640000000000000000000000000000000000000000*z)/155653774547608918949459049226626502716337609378151960029759 - 5609740340286123655179088435716554752000000000000000000000000000000000000000000000/1195576642300184106450794957109718167364189177633585204988578879, z, 9)^7)/9559849246854400988416049152000000000000000000000000000000000000 + (396296674606146645530500829518543553646142187501647739204239*root(z^9 + (876723486400000*z^8)/202893300079 + (12991106484046625280000000000*z^7)/2166615327207744284539 + (76083178071679839453913088000000000000000*z^6)/23136407038890612331350973009399 + (150940543804112324360187616985088000000000000000000000*z^5)/247064314531132675315834249803401104970659 + (4108029355821456200801735089921720320000000000000000000000000*z^4)/343483880984367044317267039965926223597613351999 - (2813441280502164056685917619200458752000000000000000000000000000000*z^3)/2638299689840923267400928133978279323453268156704319 - (1047142599503041327543418476239519744000000000000000000000000000000000000*z^2)/20264779917668131616906528997087163483444552711645874239 - (129725245369116609526016420075945328640000000000000000000000000000000000000000*z)/155653774547608918949459049226626502716337609378151960029759 - 5609740340286123655179088435716554752000000000000000000000000000000000000000000000/1195576642300184106450794957109718167364189177633585204988578879, z, 9)^8)/23157778815580100954339037465804800000000000000000000000000000000000000000 - (139017318585762447971847*root(z^9 + (876723486400000*z^8)/202893300079 + (12991106484046625280000000000*z^7)/2166615327207744284539 + (76083178071679839453913088000000000000000*z^6)/23136407038890612331350973009399 + (150940543804112324360187616985088000000000000000000000*z^5)/247064314531132675315834249803401104970659 + (4108029355821456200801735089921720320000000000000000000000000*z^4)/343483880984367044317267039965926223597613351999 - (2813441280502164056685917619200458752000000000000000000000000000000*z^3)/2638299689840923267400928133978279323453268156704319 - (1047142599503041327543418476239519744000000000000000000000000000000000000*z^2)/20264779917668131616906528997087163483444552711645874239 - (129725245369116609526016420075945328640000000000000000000000000000000000000000*z)/155653774547608918949459049226626502716337609378151960029759 - 5609740340286123655179088435716554752000000000000000000000000000000000000000000000/1195576642300184106450794957109718167364189177633585204988578879, z, 9))/275828638800776000000 - 13659982847852236349/3498414423099010
>> vpa(solT.x1)
ans =
3.0357213552334732731457027523516 + 0.0057708150473315784314972680001142i
3.0357213552334732731457027523516 - 0.0057708150473315784314972680001142i
-0.066172688730812314034716339121309
1.1009658497172078556813780942382
0.03189275258759005950150696592886
1.0071597729247286803574536258657
-0.0018153581457940921327392971755925
3.0710092676143639617828665903711
1.0009873068254378108401376768815
However, you must question how meaningful it is to give an exact solution for equations involving inexact numbers such as 9.05, which represents the complete range [9.045, 9.055)
Katy Skillings
on 17 Jul 2019
Thank you. I attempted solving another way and got this answer as well but was intimidated by the lengthy answer. What is vpa?
Walter Roberson
on 17 Jul 2019
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