Question

I just need the answer and work it asks for

Answer 1

Let's interpret each of the inequalities indepndently and then interpret them together to answer the questions in this problem.

The first inequality,

`y>-4x-1`

is asking us to consider the line with solpe -4 that goes through the point on the y-axis y=-1, and then consider the area above this line, without considering the line itself:

The second inequality,

`y<(3)/(2)x-1`

is asking us to consider the line with slope 3/2 that goes through the point in the y-axis y=-1, and then consider the area below this line, once again, without considering the line itself:

Now, the solution to the system of inequalities will be the region in which the areas of both inequalities overlap:

In this graph, the brown-ish region represents the solution to the system of inequalities. The lines are dotted because they are not part of the solution.

This is the answer to Part A.

Now, for Part B, let's locate the point (-1,-1):

As we can see, it falls outside the solution region of the system. A mathematical justification would be to plug these values into one of the inequalities, for example the first, and analize the results:

`-1>-4(-1)-1\Rightarrow-1>4-1\Rightarrow-1>3`

Since this is clearly false, we can conclude that (-1,-1) is not included in the solution area for the system.