Question

Solve the system of two linear inequalities graphically.ſr<62-3Step 2 of 3 : Graph the solution set of the second linear inequality.AnswerKeyboThe line will be drawn once all required data is provided and will update whenever a value is updated. The regions will be added once the line is drawn.Enable Zoom/PanChoose the type of boundary line:Solid (-) Dashed (-)Enter two points on the boundary line:510-35Select the region you wish to be shaded:

Answer 1

Answer and Explanation:

Given the system of two linear inequalities;

`\begin{gathered} x<6 \\ x\ge-3 \end{gathered}`

To solve the above system of inequalities graphically, we follow the below steps;

Step 1: Graph the first inequality;

Since the first inequality has a less than sign, we'll shade the region to the left of the line.

Also, the first inequality does not have an equality sign, so the line will be a dashed line.

See below the graph of the first inequality;

Step 2: Graph the second inequality on the same grid;

Since the inequality has an equality sign, the line will be a solid line.

Also, the inequality has the greater than sign, so we'll shade the region to the right of the line

See below the image of the graph;

Step 3: The solution set of the two systems of inequalities is the region where the shading overlaps.

As can be seen in the above graph, the shaded region between the dashed line and the solid line is the solution of the system of inequalities.

The graph of the solution set of the second inequality is as shown below;

On the boundary line we can select the below points;

`\begin{gathered} \lparen-3,5) \\ \lparen-3,-5) \end{gathered}`