Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions:
y < 4x − 8 y is greater than or equal to negative 5 over 2 times x plus 5
part a: describe the graph of the system, including shading and the types of lines graphed. provide a description of the solution area. (6 points)
part b: is the point (5, −8) included in the solution area for the system? justify your answer mathematically. (4 points)
show all your work !

Part A: The graph of given system of inequities is shown below.

Part B: (5, −8) is not included in the solution area for the system.

Step-by-step explanation:

The given inequalities are

Part A:

The related equations for the given inequalities are

Slope intercept form of a line is

where, m is slope and b is y-intercept.

On comparing the related equation with slope intercept form, we get

The slope of line 1 is 4 and y-intercept is -8.

The slope of line 2 is -5/2 and y-intercept is 5.

Table of values are

Line 1                   Line 2

x     y                   x        y

0    -8                  0       5

2     0                  2      0

Using these order pairs plot both line on a coordinate plane.

First line is dotted because the sign of inequality is <.

second line is dotted because the sign of inequality is ≥.

Check both inequalities by (0,0).

False

False

It means (0,0) is not included in the shaded region of any line.

The graph of given system of inequities is shown below.

Part B:

We need to check whether (5,-8) is included in the solution area for the system.

Substitute x=5 and y=-8 in inequality (1).

This statement is true. It means (5,-8) is included in the shaded area of inequality (1).

Substitute x=5 and y=-8 in inequality (2).

This statement is false. It means (5,-8) is not included in the shaded area of inequality (2).

Therefore, (5, −8) is not included in the solution area for the system.

astronomers is your final answer! : )