Question

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

y > −4x − 1
y is less than 3 over 2 times x minus 1

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 (−1, −1) included in the solution area for the system? Justify your answer mathematically. (4 points)

(10 points)

Answer 1

Check below

Explanation:

Hi there let's graph.

`y>-4x-1\\ y<(3)/(2) x-1`

(Check below)

A) Looking at the pair of inequalities, the solutions is the interval that have the common points that satisfy both inequalities. Look at the graph for the point (6,4) this point satisfy both inequalities.

Plugging in those values (6,4)

`4>-4(6)-1\\4>-25 \\\\`

Similarly for the second inequality

`4 < 3/2(6)-1\\4<8`

Since the signal is lesser (<) and greater than (>) the lines are dashed.

B) No. (-1,-1) does not belong to any of those intervals. Check below. By the same procedure above. Check it out algebraically:

-1>4-1

-1>3 False!

And

-1<-3/2-1

-1<-1 False