Question

Graph the system of inequalities presented here then use your graph to answer the following questions:

y > 5x + 5
y is greater than negative 1 over 2 times x plus 1

Part A: Graph both equations and use 2 different colors to shade. Use a 3rd color to show the solution area. Describe the graph of the system, including shading and the types of lines graphed (dotted or solid lines). Provide a description of the solution area.

Part B: Is the point (-2, 5) included in the solution area for the system? Justify your answer mathematically.

Please help. I'm so sick today that I can't think and just need to finish my homework

Answer 1

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

Part B) The ordered pair is a solution of the system of inequalities (is included in the solution area for the system)

Explanation:

Part 1) Graph the system of inequalities

we have

`y> 5x+5` ----> inequality A

The solution of the inequality A is the shaded area above the dashed line
`y=5x+5`

The slope pf the dashed line A is positive m=5

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

The x-intercept of the dashed line A is (-1,0)

`y>-(1)/(2)x+1` ----> inequality B

The solution of the inequality B is the shaded area above the dashed line
`y=-(1)/(2)x+1`

The slope pf the dashed line B is negative m=-1/2

The y-intercept of the dashed line B is (0,1)

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

The solution of the system of inequalities is the shaded area above the dashed line A and above the dashed line B

using a graphing tool

see the attached figure

Part B) Is the point (-2, 5) included in the solution area for the system? Justify your answer mathematically

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 and the value of y in each inequality

For x=-2, y=5

Verify inequality A

`5>5(-2)+5`

`5>-5` ---> is true

so

The ordered pair satisfy inequality A

Verify inequality B

`5>-(1)/(2)(-2)+1`

`5>2` ---> is true

so

The ordered pair satisfy inequality B

therefore

The ordered pair is a solution of the system of inequalities (is included in the solution area for the system)