Question

Please actually answer and not just take my points and answer quick this is timed

Graph the system of inequalities presented here on your paper, then use your graph to answer the following questions.
Y<4x-8
Y_>-5/2x+5
Part A: Describe the graph of the system including shading and the types of lines Graphed Provided a description of the solution area
Part B: is the point (5, -8)Included in the solution area for the system? Justify your answer mathematically

Answer 1

Part A) The graph in the attached figure (see the explanation)

Part B) The ordered pair is not included in the solution area for the system (see the explanation)

Explanation:

Part A) we have

`y&lt;4x-8` ----> inequality A

The solution of the inequality A is the shaded area below the dashed line
`y=4x-8`

The slope of the dashed line is positive

The y-intercept of the dashed line is (0,-8)

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

`y\geq -(5)/(2)x+5` ----> inequality B

The solution of the inequality B is the shaded area above the solid line
`y=-(5)/(2)x+5`

The slope of the solid line is negative

The y-intercept of the solid line is (0,5)

The x-intercept of the solid line is (2,0)

The solution of the system of inequalities is the shaded area between the dashed line and the solid line

see the attached figure

Part B) is the point (5, -8) 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

Substitute the value of x=5, y=-8 in each inequality and then analyze the results

Inequality A

`-8&lt;4(5)-8`

`-8&lt;12` ----> is true

so

the ordered pair satisfy inequality A

Inequality B

`-8\geq -(5)/(2)(5)+5`

`-8\geq -7.5` ---> is not true

so

the ordered pair not satisfy the inequality B

therefore

The ordered pair is not included in the solution area for the system