Derive values of alphabet

Need to save the below alphabet values, How could I build the matlab code?

a=0.25

a+b+e=0

7a+6b+c+5e+f=0

19a+13b+5c+d+9e+3f=0

25a+12b+8c+4d+7e+3f=0

16a+4b+4c+4d+2e+f=0

Answer 1

[DGM]

For a numerical approach:

https://www.mathworks.com/help/matlab/math/systems-of-linear-equations.html

% coefficient matrix
A = [1 0 0 0 0 0;
    1 1 0 0 1 0;
    7 6 1 0 5 1;
    19 13 5 1 9 3;
    25 12 8 4 7 3;
    16 4 4 4 2 1];
% sums
b = [0.25 0 0 0 0 0].';

% solve for variables
x = A\b

x = 6×1

0.2500 -2.0000 1.0000 -1.0000 1.7500 0.5000