Solve the indeterminate system:
$a=3f$
$3b=10f+9g$
$3c=10f+10g+9h$
$3d=10f+10g+10h+9i$
$3e=10f+10g+10h+10i+9j$
$3e=-j$
EDIT: Please don't close it, I actually want to learn. This is a challenge homework problem, not standard homework. I've tried everything but it seems impossible to do by hand because it gets too messy. I might be doing it the wrong way, so I wanted to see how you guys would do it. Thanks!
This is how it was stated originally, if it helps:
$a=3f$
$3b=3a+f+9g$
$3c=3b+g+9h$
$3d=3c+h+9i$
$3e=3d+i+9j$
$3e+j=0$
Hint: work with everything on the RHS (subtract $a$ from both sides of the first equation, $3b$ from both sides of the second equation, etc). Use gaussian elimination with the matrix: $$\begin{pmatrix} -1 & 0 & 0 & 0 & 0 & 3 & 0 & 0 & 0 & 0 \\ 0 & -3 & 0 & 0 & 0 &10 & 9 & 0 & 0 & 0 \\0 & 0 & -3 & 0 & 0 & 10 & 10 & 9 & 0 & 0 \\ 0 & 0 & 0 & -3 & 0 & 10 & 10 & 10 & 9 & 0 \\ 0 & 0 & 0 & 0 & -3 & 10 & 10 & 10 & 10 & 9 \\ 0 & 0 & 0 & 0 & -3 & 0 & 0 & 0 &0 & -1\end{pmatrix}$$
(the problem is given half solved, if you think about it)