Question

graph the solution set of the following system of inequalities.
2x + 4y ≤ 4
4x + 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 $2x + 4y\leq4$, solve for $y$:
$4y\leq - 2x + 4$, then $y\leq-\frac{1}{2}x + 1$.
For $4x + y\leq8$, solve for $y$:
$y\leq - 4x+8$.

Step2: Graph the boundary lines

The boundary line of $y =-\frac{1}{2}x + 1$ has a $y$-intercept of $1$ and a slope of $-\frac{1}{2}$. Since the inequality is $y\leq-\frac{1}{2}x + 1$, we draw a solid line (because of the $\leq$ sign) and shade below the line.
The boundary line of $y=-4x + 8$ has a $y$-intercept of $8$ and a slope of $-4$. Since the inequality is $y\leq - 4x+8$, we draw a solid line and shade below the line.
The solution set is the region that is shaded for both inequalities.

Answer:

Graph the solid line $y =-\frac{1}{2}x + 1$ and shade below it, graph the solid line $y=-4x + 8$ and shade below it. The overlapping shaded region is the solution set.