Question

graph the solution of the system of linear inequalities. x - y≥1 x + y≤8 use the graphing tool to graph the system of inequalities. click to enlarge graph

Explanation:

Step1: Rewrite inequalities in slope - intercept form

For $x - y\geq1$, rewrite as $y\leq x - 1$. For $x + y\leq8$, rewrite as $y\leq -x + 8$.

Step2: Graph the lines

Graph $y=x - 1$ as a solid line (since $\geq$ includes equality). Its $y$-intercept is - 1 and slope is 1. Graph $y=-x + 8$ as a solid line (since $\leq$ includes equality). Its $y$-intercept is 8 and slope is - 1.

Step3: Determine the shaded regions

For $y\leq x - 1$, shade below the line $y=x - 1$. For $y\leq -x + 8$, shade below the line $y=-x + 8$. The solution of the system is the intersection of the two shaded regions.

Answer:

The solution is the intersection of the region below the line $y = x-1$ and the region below the line $y=-x + 8$, including the lines themselves.