Q. 33 - 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:

$\left\{\begin{array}{l}2x+3y\ge 6\\ 2x+3y\le 0\end{array}\right.$

Step-by-Step Solution

Answer

The graph of the given system of inequality do not exist.

Step 1. Graph of the line 2 x + 3 y ≥ 6

To plot the graph of $2x+3y\ge 6$, plot the line $2x+3y=6$.

Take any arbitrary point $(0,0)$

Since the taken point does not satisfy the inequality, therefore, the shaded region will not include this point.

Step 2. Graph of the inequality 2 x + 3 y ≤ 0

The graph of the inequality $2x+3y\le 0$ can be drawn by graphing $2x+3y=0$

Take any arbitrary point $(2,0)$

The given inequality does not satisfy this point.

Thus, the shaded region will not include this point.

Step 3. Final Graph

The intersection of both the graphs will give the final graph of the system of inequalities.

Since, there is no intersection, Hence, the graph of the given system of inequalities does not exist.