Question

Graph the system of linear inequalities.

Answer 1

Step 1 :

The system of linear inequalities are and .

1) Draw the coordinate plane.

First linear inequality is .

Rewrite the inequality as .

2) Graph the line .

3) Since the inequality symbol is , the boundary is included in the solution set.

Graph the boundary of the inequality with solid line.

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

A simple chioce is .

Substitute and in original inequality.

The statement is true.

5) Since the statement is true, shade the region that contains the point , shaded in fuchsia colour.

Step 2 :

The second linear inequality is .

Rewrite the inequality as .

6) Graph the line.

7) Since the inequality symbol is , the boundary is included in the solution set.

Graph the boundary of the inequality with solid line.

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

A simple chioce is .

Substitute and in original inequality.

The statement is false.

9) Since the statement is false, shade the region that does not contains the point , shaded in aqua colour.

Graph of the system of linear inequalities is :

The solution of the system is the set of ordered pairs in the intersection of the graphs of and . This region is shaded in light purple color.

Solution :

Graph of the system of linear inequalities is :