Question

write a system of linear inequalities for the given graph.

Answer 1

Step 1 :

Observe the graph, is a solid line.

To determine which symbol to be used to write the linear inequality, take a test point in either half- plane.

A simple chioce is .

Substitute in .

Since the line is solid line, take the inequality symbol as .

Thus, the linear inequality is .

Step 2 :

Observe the graph, is a solid line.

To determine which symbol to be used to write the linear inequality, take a test point in either half- plane.

A simple chioce is .

Substitute in .

Since the line is solid line, take the inequality symbol as .

Thus, the linear inequality is .

Step 3 :

Find the solid line passing through the points and .

Let the points be and .

Line equation passing through two points is .

Substitute the points and in above equation.

To determine which symbol to be used to write the linear inequality, take a test point in either half- plane.

A simple chioce is .

Substitute and in the line equation .

Since the line is solid line, take the inequality symbol as .

Thus, the linear inequality is .

 

Answer 2

Contd.....

Step 4 :

Find the solid line passing through the points and .

Let the points be and .

Line equation passing through two points is .

Substitute the points and in above equation.

To determine which symbol to be used to write the linear inequality, take a test point in either half- plane.

A simple chioce is .

Substitute and in the line equation .

Since the line is solid line, take the inequality symbol as .

Thus, the linear inequality is .

Step 5 :

Observe the graph, take all values of x , whom greater than equals to zero.

Thus, the linear inequality is .

Thus, the system of linear inequalities for the given graph is .

Solution :

The system of linear inequalities for the given graph is .