Find the linear inequalities for which the shaded region in the given figure is the solution set.

(N/A) $1$. Consider the line $x+y=4$. This line intersects the $X$-axis at $(4,0)$ and the $Y$-axis at $(0,4)$. Testing the origin $(0,0)$,we see $0+0 \leq 4$ is false,so the region is on the side away from the origin,giving $x+y \geq 4$.
$2$. Consider the line $x+y=8$. This line intersects the $X$-axis at $(8,0)$ and the $Y$-axis at $(0,8)$. Testing the origin $(0,0)$,we see $0+0 \leq 8$ is true,so the region is on the side containing the origin,giving $x+y \leq 8$.
$3$. The vertical line $x=5$ intersects the $X$-axis at $(5,0)$. The shaded region is to the left of this line,giving $x \leq 5$.
$4$. The horizontal line $y=5$ intersects the $Y$-axis at $(0,5)$. The shaded region is below this line,giving $y \leq 5$.
$5$. Since the shaded region is in the first quadrant,we have $x \geq 0$ and $y \geq 0$.
Thus,the system of linear inequalities is $x+y \geq 4, x+y \leq 8, x \leq 5, y \leq 5, x \geq 0, y \geq 0$.