Question

Graph the system of linear inequalities.Tell whether the graph is bounded or unbounded,and label the corner points.

Answer 1

Step 1:

The system of inequalities are and .

Now graph the all of four constraints.

Draw the coordinate plane.

The inequality .

Graph the line .

 Since the inequality symbol is the boundary is included the solution set.

Graph the boundary of the inequality with solid line.

To determine which half plane to be shaded use a test point in either half- plane.

A simple choice is . Substitute in original inequality.

The statement is true.

Since the statement is true, shade the region contain point .

The inequality .

Graph the line .

Since the inequality symbol is the boundary is included the solution set.

Graph the boundary of the inequality with solid line.

To determine which half plane to be shaded use a test point in either half- plane.

A simple choice is . Substitute in original inequality.

The statement is true.

Since the statement is true, shade the region contain point .

The inequality .

Graph the line .

Since the inequality symbol is the boundary is included the solution set.

Graph the boundary of the inequality with solid line.

To determine which half plane to be shaded use a test point in either half- plane.

A simple choice is . Substitute in original inequality.

The statement is false.

Since the statement is false, shade the region does not contain point .

Answer 2

Contd ...

And the inequality .

Graph the line .

Since the inequality symbol is the boundary is included the solution set.

Graph the boundary of the inequality with solid line.

To determine which half plane to be shaded use a test point in either half- plane.

A simple choice is . Substitute in original inequality.

The statement is true.

Since the statement is true, shade the region contain point .

Step 2:

Graph:

The feasible area looks like in the graph.

Observe the graph: The corner points are .

The graph of the system of linear inequalities is bounded.

Solution:

The graph of the system of linear inequalities is bounded.

The corner points are .