TL;DR Solve a 9x9 matrix without negative solutions.
To make one thing clear! - I have no idea what I'm doing.
What I do know however is to reproduce an equation with different coefficients every time. More specific - this is a game where I'm offered to purchase a set of weapons for a price. I will always get atleast 1 of each weapon, there are 9 types.
So I know how much the total cost is, and how many I get of each - I want to know the individual prices that the swords are sold for.
This is what I think of; where $a$ through $k$ are known.
$ax_1 + bx_2 + cx_3 + dx_4 + ex_5 + fx_6 + gx_7 + hx_8 + jx_9 = k$
I tried using this website at the 9x9 calculator, entered 9 different equations and got values for each $x_i$, $i\in[1,9]$. The problem is that some of the values were negative.
How do I solve this without getting negative values?
Just realized I'd misread the original question. You do have the numbers of weapons but not the prices of each. (The problem of finding possible numbers of weapons for known prices is more interesting.)
If your equation data is valid, then you ought not to get negative $x_i$ values. I never used the site you link to but it seemingly works for 2 x 2 systems. Are you sure you are entering the correct equation data ? If you are and you still get even one negative $x_i$ then the data is invalid.