Question

graph the solution set of the given system of linear inequalities.
3x + y < 6
x - y > 3
use the graphing tool to graph the system.

Explanation:

Step1: Rewrite inequalities in slope - intercept form

For $3x + y<6$, rewrite as $y < - 3x+6$. The boundary line is $y=-3x + 6$, which has a slope of $-3$ and a $y$-intercept of $6$. Since it is $y < - 3x+6$, we will draw a dashed line (because the inequality is strict) and shade below the line.
For $x - y>3$, rewrite as $y

Step2: Find the intersection region

The solution set of the system is the region that satisfies both inequalities. This is the region that is below both $y=-3x + 6$ and $y=x - 3$.

Answer:

Graph the dashed line $y=-3x + 6$ and shade below it. Graph the dashed line $y=x - 3$ and shade below it. The intersection of the two shaded regions is the solution set of the system of linear inequalities.