Q. 29 - Precalculus Enhanced with Graphing Utilities

Question

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

$\left\{\begin{array}{r}x-2y\le 6\\ 2x-4y\ge 0\end{array}\right.$

Step-by-Step Solution

Answer

The graph is 

Step 1. Graphing line x - 2 y ≤ 6

The graph of the line $x-2y\le 6$ can be plotted by plotting the line$x-2y=6$

Now, the graph is shaded including the origin because it satisfies the point $(0,0)$

Step 2. Graphing line 2 x - 4 y ≥ 0

First graph the line$2x-4y=0$$2x-4y=0$

Take any arbitrary point $(2,0)$.

Since the equation satisfies this point, therefore, it will come in the shaded region.

Step 3. Final graph

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