Question

Determine which shaded region corresponds to the solution region of the system of linear inequalities? (multiple choice)?

x + 4y ≥ 4 
x + y ≥ 2 
x ≥ 0 
y ≥ 0

Answer 1

The linear inequalities are x + 4y ≥ 4 , x + y ≥ 2 , x ≥ 0  and y ≥ 0

Draw the coordinate plane.

First inequality x + 4y ≥ 4 .

Related equation x + 4y = 4

Slope intercept form y = - x/4 + 1

• Graph the line y = - x/4 + 1
• Since the inequality symbol is ≥ the boundary is  included the solution set.
• Graph the boundary of the inequality x + 4y ≥ 4 with solid line.
• To determine which half plane to be shaded use a test point in either half- plane.
• A simple chioce is (0,0). Substitute x  = 0 and y  = 0 in original inequality

x + 4y ≥ 4

0 ≥ 4

The statement is false.

• Since the statement is false , shade the region that does not contain point (0,0)

Second inequality x + y ≥ 2.

• Related equation x + y = 2
• Slope intercept form y = - x + 2
• Graph the line y = - x + 2
• Since the inequality symbol is ≥ the boundary is  included the solution set.
• Graph the boundary of the inequality x + y ≥ 2 with solid line.
• To determine which half plane to be shaded use a test point in either half- plane.

A simple chioce is (0,0). Substitute x  = 0 and y  = 0 in original inequality

x + y ≥ 2

0 ≥ 2

The statement is false.

• Since the statement is false , shade the region that does not contain point (0,0)

Third inequality x ≥ 0.

Related equation x = 0

• Graph the line x = 0
• Since the inequality symbol is ≥ the boundary is  included the solution set.
• Graph the boundary of the inequality x ≥ 0 with solid line.
• To determine which half plane to be shaded use a test point in either half- plane.

A simple chioce is (1,1). Substitute x  = 1 and y  = 1 in original inequality

x ≥ 0

1 ≥ 0

The statement is true.

• Since the statement is true , shade the region contain point (1,1)

shaded in aqua colour.

Fourth inequality y ≥ 0.

Related equation  y = 0

• Graph the line y = 0
•  Since the inequality symbol is ≥ the boundary is included the solution set.
• Graph the boundary of the inequality y ≥ 0 with solid line.
• To determine which half plane to be shaded use a test point in either half- plane.

A simple chioce is (1,1). Substitute x  = 1 and y  = 1 in original inequality

y ≥ 0

1 ≥ 0

The statement is true.

• Since the statement is true , shade the region contain point (1,1)

Graph

The solution of the systemo f linear inequalities is the set of ordered pairs in the intersection of the graph of x + 4y ≥ 4 , x + y ≥ 2 , x ≥ 0  and y ≥ 0. This region is shaded in dark pink color.

Graph C is correct choice.