graph the feasible set of the system of linear inequalities. shade the feasibility region

Question

x+2y>(or=)4

2x-y>(or=)6

Answer 1

Step 1:

The system of inequalities are and .

Draw the coordinate plane.

Consider 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 is to be shaded, consider a test point in either of the half- plane.

Test point is .

Substitute in .

.

The statement is true.

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

Step 2:

Consider 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 is to be shaded, consider a test point in either of the half- plane.

Test point is .

Substitute in .

.

The statement is true.

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

Graph:

Graph the inequalities: and .

Shade the required region.

Step 3:

Feasible Region:

The graph of the inequalities and is the shaded region, where every point in the shaded region satisfies the both the inequalities.

Graph:

Shade the feasible region:

Solution:

Graph of the region bounded by the system of inequalties is

.