# Solving linear system of equations

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Rick on 5 Mar 2015
Answered: John D'Errico on 5 Mar 2015
Hello,
I want to solve a system of linear equations, but there is a slight twist in the equation (i.e. not every one is written Ax = B). How can I use matlab to solve this? I want to know xH. I suppose I will use linsolve command, but I don't know what exact manipulation will need to be made. Thanks
% Vapor Pressure of n-Hexane (kPa)
PH = zeros(5,1);
PH(1) = 101.3;
PH(2) = 136.7;
PH(3) = 197.3;
PH(4) = 284.0;
PH(5) = 456.0;
% Vapor Pressure of n-Octane (kPa)
PO = zeros(5,1);
PO(1) = 16.1;
PO(2) = 23.1;
PO(3) = 37.1;
PO(4) = 57.9;
PO(5) = 101.3;
% Liquid Mole fraction of n-Hexane in n-Hexane/n-Octane mixture
xH = zeros(5,1);
xH(1)*PH(1) + (1-xH(1))*PO(1) - 101.32 = 0;
xH(2)*PH(2) + (1-xH(2))*PO(2) - 101.32 = 0;
xH(3)*PH(3) + (1-xH(3))*PO(3) - 101.32 = 0;
xH(4)*PH(4) + (1-xH(4))*PO(4) - 101.32 = 0;
xH(5)*PH(5) + (1-xH(5))*PO(5) - 101.32 = 0;

Torsten on 5 Mar 2015
xH(1)=(101.32-PO(1))/(PH(1)-PO(1))
xH(2)=(101.32-PO(2))/(PH(2)-PO(2))
xH(3)=(101.32-PO(3))/(PH(3)-PO(3))
xH(4)=(101.32-PO(4))/(PH(4)-PO(4))
xH(5)=(101.32-PO(5))/(PH(5)-PO(5))
Best wishes
Torsten.

### More Answers (1)

John D'Errico on 5 Mar 2015
Or, even simpler in one line for the solve, and one line each to define each of PO and PH...
PH = [101.3; 136.7; 197.3; 284.0; 456.0];
PO = [16.1; 23.1; 37.1; 57.9; 101.3];
xH = (101.32 - PO)./(PH - PO);
Learn to use vectors and arrays in MATLAB. Until then, you will find yourself writing far less efficient code, and spending far more time just writing the code.