Question

Graph the system of inequalities.

Answer 1

Step 1:

The system of inequalities are and .

Consider .

The graph of the inequality is the shaded region, where every point in the shaded region satisfies the inequality.

Since the inequality symbol is , the boundary is drawn as a solid circle to show that points on the circle satisfies the inequality and the shaded region along with the solid circle of the graph   is the solutions to the inequality.

Test Point:

Since the above statement is true, shade the region inside the circle.

Step 2:

Consider .

The graph of the inequality is the shaded region, where every point in the shaded region satisfies the inequality.

Since the inequality symbol is , the boundary is drawn as a solid line to show that points on the satisfies the inequality and the shaded region along with the solid line of the graph   is the solutions to the inequality.

Test Point:

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

Answer 2

Contd...

Step 3:

The solution of the system is the set of ordered pairs in the intersection of the graphs of  and .

Test Point:

and

and

and .

Since both statement are true, shade the region containing the point .

Step 4:

Graph:

Draw the coordinate plane.

Graph the system of inequalities and .

Plot the points , and .

Shade the required regions.

Observe the graph:

The region shaded violet in color along with the circle indicates the inequality solution of the .

The region shaded green in color along with the line indicates the inequality solution of the .

The region shaded blue in color indicates the intersection part of the two inequalities.

Solution:

The graph system of inequalities are and is