Question

graph the solution set of the given system of linear inequalities.
4x + y < 8
x - y > 5
use the graphing tool to graph the system.

Explanation:

Step1: Rewrite first inequality in slope - intercept form

Rewrite $4x + y<8$ as $y < - 4x+8$. The boundary line is $y=-4x + 8$, which has a y - intercept of 8 and a slope of - 4. Since the inequality is $y < - 4x+8$, we will draw a dashed line (because the inequality is strict) and shade the region below the line.

Step2: Rewrite second inequality in slope - intercept form

Rewrite $x - y>5$ as $y

Step3: Find the intersection region

The solution set of the system of inequalities is the region that is shaded for both inequalities.

Answer:

Graph the dashed line $y=-4x + 8$ and shade below it, graph the dashed line $y=x - 5$ and shade below it. The solution set is the intersection of the two shaded regions.