Solving equation System

Question

I've been trying to solve this equation, but I can't get it. There's a term in the equation, $m(9.81)$, and can't handle it with the other terms of the equation. And $F_{AB} = 1000$.

$$ \begin{gather} -\frac{2}{7} F_{AB} - \frac{1}{3} F_{AC} + \frac{3}{5} F_{AD} = 0 \\ \frac{3}{7} F_{AB} - \frac{2}{3} F_{AC} - \frac{4}{5} F_{AD} = 0 \\ \frac{6}{7} F_{AB} + \frac{2}{3} F_{AC} - m(9.81) = 0 \end{gather} $$

For reference, the original image: https://i.stack.imgur.com/WBkza.png

Answer 1

Eq.1 $-\frac12 $ Eq. 2 eliminates $F_{AC}$ and gives $F_{AD}=500$. Then you can compute $F_{AC}=\frac{300}7$ from the first equation, and finally the third equation will give you $m$.

Answer 2

Hint: Given that you know one of the terms already ($F_{AB} = 1000$), the system reduces to 3 variables: $F_{AC}$, $F_{AD}$, and $m$. Then you can find $F_{AC}$ and $F_{AD}$ with the first 2 equations, and then finally $m$ with the last.