Graph the feasible region for the following system of inequalities.
\[
\begin{array}{l}
x+y \leq 5 \\
x-y \geq 6
\end{array}
\]

Use the graphing tool on the right to graph the system of inequalities.

Step 1 ：Rewrite the inequality \(x + y \leq 5\) as \(y \leq -x + 5\). This is a linear equation in slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. The slope is -1 and the y-intercept is 5.

Step 2 ：Graph the inequality by starting at the point \((0,5)\) on the y-axis and moving down one unit and to the right one unit for each subsequent point. Because the inequality is \("less than or equal to"\), draw a solid line to represent the equation. The region below the line (including the line itself) represents the solutions to the inequality.

Step 3 ：Rewrite the inequality \(x - y \geq 6\) as \(y \leq x - 6\). This is a linear equation in slope-intercept form. The slope is 1 and the y-intercept is -6.

Step 4 ：Graph the inequality by starting at the point \((0,-6)\) on the y-axis and moving up one unit and to the right one unit for each subsequent point. Because the inequality is \("greater than or equal to"\), draw a solid line to represent the equation. The region below the line (including the line itself) represents the solutions to the inequality.

Step 5 ：The feasible region is the area where the solutions to both inequalities overlap. In this case, it is the area below both lines.