# Why am I getting error:- Empty sym: 0-by-1

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KAJAL KUMARI on 8 Jul 2021
Answered: Walter Roberson on 9 Jul 2021
I am trying to get the values of variables using vpasolve.
syms n1 n2 n3 n4 n5 n6 n7 n8 n9 n10 n11 n12 n13 n14 n15 n16 n17 K
eqn1 = ((0.2)^3).*n1 + ((0.22)^3).*n2+((0.23)^3).*n3+ ((0.24)^3).*n4 + ((0.25)^3).*n5+((0.26)^3).*n6+((0.27)^3).*n7+((0.28)^3).*n8+((0.29)^3).*n9+((0.3)^3).*n10+((0.31)^3).*n11+((0.32)^3).*n12+((0.34)^3).*n13+((0.35)^3).*n14+((0.4)^3).*n15+((0.42)^3).*n16+((0.45)^3).*n17==K;
eqn2 = ((0.2)^3).*n1/K==1;
eqn3 = ((0.22)^3).*n2/K==1.5;
eqn4 = ((0.23)^3).*n3/K ==4;
eqn5 = ((0.24)^3).*n4/K ==7;
eqn6 = ((0.25)^3).*n5/K ==11.4;
eqn7 = ((0.26)^3).*n6/K ==13.8;
eqn8 = ((0.27)^3).*n7/K ==15;
eqn9 = ((0.28)^3).*n8/K ==12;
eqn10 = ((0.29)^3).*n9/K ==8;
eqn11 = ((0.3)^3).*n10/K == 4.5;
eqn12 = ((0.31)^3).*n11/K ==2.5;
eqn13 = ((0.32)^3).*n12/K ==1.4;
eqn14 = ((0.34)^3).*n13/K ==1;
eqn15 = ((0.35)^3).*n14/K ==0.5;
eqn16 = ((0.4)^3).*n15/K ==0.2;
eqn17 = ((0.42)^3).*n16/K ==0.1;
eqn18 = ((0.45)^3).*n17/K==0.02;
eqn19 = n1+n2+n3+n4+n5+n6+n7+n8+n9+n10+n11+n12+n13+n14+n15+n16+n17 == 7.68e8;
eqns = [eqn1,eqn2,eqn3,eqn4,eqn5,eqn6,eqn7,eqn8,eqn9,eqn10,eqn11,eqn12,eqn13,eqn14,eqn15,eqn16,eqn17,eqn18,eqn19];
vars = [n1 n2 n3 n4 n5 n6 n7 n8 n9 n10 n11 n12 n13 n14 n15 n16 n17 K];
Sharmin Kibria on 9 Jul 2021
I believe the system of equations do not have a solution. Check the second tip in the following.

Walter Roberson on 9 Jul 2021
There is no solution.
You have 19 equations in 18 variables.
If you solve the middle 17 equations using solve() you get solutions for the n* variables in terms of K.
When you substitute those into the first equation, you get an expression in K on the left and an expression in K on the right. The only solution for that is K = 0. Substituting K = 0 into the solutions to the middle 17 shows they must all be 0 as well.
But making the variables all 0 does not satisfy the final equation. So, no solution.

R2021a

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