Question

Find the intersection point (if there is one) and graph shading the appropriate areas:
x+y >=0 and 2x+y<=4

Answer 1

Given inequalities are x + y >= 0 and 2x + y <= 4.

1) Draw the coordinate plane.

First inequality is x + y >= 0.

2)The graph of the inequality x + y >= 0 is the shaded region and boundary of the inequality is x + y = 0.

3) Since the inequality symbol is >= the boundary is included the solution set.

Graph the boundary of the inequality x + y >= 0 with solid line.

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

A simple chioce is (2,2). Substitute x  = 2 and y = 2 in original inequality

2 + 2 >= 0

4 >= 0

The statement is true.

5) Since the statement is true , shade the region contain point (2, 2),

Shaded in fuchsia colour.

Second inequality is 2x + y <= 4.

6)The graph of the inequality 2x + y <= 4 is the shaded region and boundary of the inequality is 2x + y = 4.

7) Since the inequality symbol is <= the boundary is included the solution set.

Graph the boundary of the inequality 2x + y <= 4 with solid line.

8) 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

2(0) + 0 <= 4

0 + 0 <= 4

0 <= 0.

The statement is true.

9) Since the statement is true, shade the region contain the point (0,0)

shaded in aqua colour.

Graph :

The solution of the system is the set of ordered pairs in the intersection of the graph of x + y >= 0 and 2x + y <= 4. This region is shaded in light purple color.

Observe the graph, the intersection point is (4, - 4).so,this is the solution of the system of inequalities.