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

0 votes
x+2y>(or=)4

2x-y>(or=)6
asked Oct 1, 2015 in ALGEBRA 2 by egbush Rookie

1 Answer

0 votes

Step 1:

The system of inequalities are image and image.

Draw the coordinate plane.

Consider the inequality:  image.

Graph the line image.

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

Graph the boundary of the inequality imagewith solid line.

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

Test point is image.

Substitute image in image.

image

image.

The statement is true.

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

Step 2:

Consider the inequality: image

Graph the line image.

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

Graph the boundary of the inequality image 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 image.

Substitute image in image.

image

image.

The statement is true.

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

Graph:

Graph the inequalities: image and image.

Shade the required region.

image

Step 3:

Feasible Region:

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

Graph:

Shade the feasible region:

image

Solution:

Graph of the region bounded by the system of inequalties is

image.

answered Oct 1, 2015 by Sammi Mentor
edited Oct 1, 2015 by Sammi

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