Question

In Problems 23–34, graph each system of linear inequalities by hand. Verify your results using a graphing utility

$\left\{\begin{array}{l}x+4y\le 8\\ x+4y\ge 4\end{array}\right.$

Short answer

The graph is

Step-by-step solution

Step 1. Graphing line x+4y≤8

The graph of the line $x+4y\le 8$can be plotted by plotting the line $x+4y=8$Now, the graph is shaded including the origin because it satisfies the point $(0,0)$

Step 2. Graph the line x+4y≥4

The graph of the line $x+4y=4$will be plotted first.

Now, the graph is shaded excluding the origin because it does not satisfy the point (0,0)

Step 3. Final graph

The intersection of both the graphs of the lines will give the final graph.