Question

Solve each system of inequalities by graphing.

$\begin{array}{l}y\le -x-3\\ y\ge 3x-2\end{array}$

Short answer

The solution of the system of inequalities is double shaded region in the graph given below:

Step-by-step solution

Step 1. Graph the inequalities.

Here the equations are:

$y\le -x-3$and$y\ge 3x-2$

The strategy is to solve the inequalities by graphing. The graph of the system of inequalities is drawn as below:

Step 2. State interpretation of the graph.

The graph of$y=-x-3$ is solid line (the line in black) and is included in the graph of the solution. The graph of$y=3x-2$ (the line in brown) is solid line again and therefore, is included in the graph of the solution.

Step 3. State the conclusion.

The solution of the system is the set of ordered pairs in the intersection of the graphs of $y\le -x-3$ and $y\ge 3x-2$. This region is green double shaded region.