Solve the system of inequality:

Question

{(3x+y>-4@x-y>-5@x≥0)┤?

Answer 1

(3x+y>-4;x-y>-5;x≥0)

Alternate form is

 

(y>-3x-4;y<x+5;x≥0)

The solution is

(x≥0;-3x-4<y<x)

 

Answer 2

The inequalities are -3x + y > -4, x - y > -5 and x ≥ 0.

Draw the coordinate plane.

First inequality -3x + y > -4.

1) Graph the line -3x + y = -4.

2) Since the inequality symbol is >, the boundary is not included the solution set.

So graph the boundary of the inequality -3x + y > -4  with dashed line.

3) 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 -3x + y > -4

0 > -4

The statement is true. So, shade the region that contain point (0,0) with red colour.

Second inequality x - y > -5.

1) Graph the line x - y = -5.

2) Since the inequality symbol is >, the boundary is not included the solution set.

So graph the boundary of the inequality x - y > -5  with dashed line.

3) 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 > -5.

0 > -5

The statement is true. So, shade the region that contain point (0,0) with blue colour.

Third inequality x ≥ 0.

1) Graph the line x = 0.

2) Since the inequality symbol is ≥, the boundary is included the solution set.

So graph the boundary of the inequality x ≥ 0  with solid line.

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

A simple chioce is (1, 0). Substitute x  = 1 and y  = 0 in original inequality x ≥ 0.

1 > 0

The statement is true. So, shade the region that contain point (1,0) with green colour.

Graph:

The solution of the system is the set of ordered pairs in the intersection of the graph of

-3x + y > -4, x - y > -5 and x ≥ 0 i.e., x ≥ 0, -3x - 4 < y < x + 5. This region is shaded in dark green color.