For a numerical approach:
% 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
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