Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions:
y > −2x + 3
y is less than 1 over 2 times x minus 2
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 (−2, 3) included in the solution area for the system? justify your answer mathematically. (4 points)

Part A) The description of the solution area in the procedure

Part B) The ordered pair (−2, 3) is not included in the solution area for the system

Step-by-step explanation:

Part A) we have

y > -2x+3 -----> inequality A

The solution of the inequality A is the shaded area above the dashed line

y=-2x+3

The slope of the dashed line is negative (m=-2)

The y-intercept of the dashed line is (0,3)

The x-intercept of the dashed line is (1.5,0)

y < (1/2)x-2 -----> inequality B

The solution of the inequality B is the shaded area beow the dashed line

y=(1/2)x-2

The slope of the dashed line is positive (m=1/2)

The y-intercept of the dashed line is (0,-2)

The x-intercept of the dashed line is (4,0)

using a graphing tool

The solution of the system of inequalities is the shaded area between the two dashed lines

see the attached figure

Part B) Is the point (−2, 3) included in the solution area for the system?

we know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities of the system

Verify inequality A

Substitute the value of x=-2 and y=3 in the inequality A

3 > -2(-2)+3

3 > 7 -----> is not true

therefore

The ordered pair (−2, 3) is not included in the solution area for the system

the answer is:

the correct option:

b.

to solve the problem, we need to remember how to operate to simplify exponential expressions using the logarithms.

we are given the equation:

then, using placing logarith with base 7 on both sides of the equation, we have:

so, rounding the obtained result to two decimal places (nearest hundreth), we have:

hence, we have that the correct option:

b.

have a nice day!