Answer
$x_1=20-x_3$
$x_2=-100+x_3$
$x_3$ is free
$x_4=-100$Some of the flows must be negative. This is because there is no flow into C but there is a flow out. $80+x_1+x_2=0$
Work Step by Step
Write a table with intersection, flow in, and flow out
$\begin{bmatrix}
1 & 0 & 1 & 0 & 20\\
0 & 1 & -1 & -1 & 0\\
-1 & -1 & 0 & 0 & 80\\
\end{bmatrix}$ Add row 1 and row 2 to row 3
~$\begin{bmatrix}
1 & 0 & 1 & 0 & 20\\
0 & 1 & -1 & -1 & 0\\
0 & 0 & 0 & -1 & 100\\
\end{bmatrix}$ Subtract row 3 from row 2 and multiply all elements of row 3 by -1
~$\begin{bmatrix}
1 & 0 & 1 & 0 & 20\\
0 & 1 & -1 & 0 & -100\\
0 & 0 & 0 & 1 & -100\\
\end{bmatrix}$
$x_1=20-x_3$
$x_2=-100+x_3$
$x_3$ is free
$x_4=-100$
Some of the flows must be negative. This is because there is no flow into C but there is a flow out. $80+x_1+x_2=0$
