Ans: B
Substitute $(0,0)$ into the left side of the equation $y-x=1$, we have
Substitute $(0,0)$ into the left side of the equation $y-x=1$, we have
$\begin{array}{rcl}
\text{LHS} & = & (0)-(0) \\
& = & 0 \\
& \le & 1
\end{array}$
Therefore, the shaded region is a part of the solution of $y-x\ge 1$.
Substitute $(0,0)$ into the left side of the equation $x+y=6$, we have
$\begin{array}{rcl}
\text{LHS} & = & (0) + (0) \\
& = & 0 \\
& \le & 6
\end{array}$
Therefore, the shaded region is a part of the solution of $x+y\le 6$.
Since the shaded region is on the left side of the $y$-axis, then it is a part of the solution of $x\ge 0$.
By combining the above result, the shaded region is the solution of the system
$\left\{ \begin{array}{l}
y-x\ge 1 \\
x+y \le 6 \\
x \ge 0
\end{array} \right.$
