Question

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

Answer 1

It is to be noted that the Graph of the indicated inequalities is herewith attached.

What is the graph of the system?

As indicated above, this is a graph of a system of inequalities, where:

Y > -4x-1 and

y <3/2x-1

Is the point (-1,1) included in the solution area for the system?

No. the point (-1, 1) is not included in the solution area for the system.

How do we justify this mathematically?

Step 1 - Plug in (-1, 1) in to the first equation. where y = -1 and x = 1.

Hence,

-1 > -4(1) -1

4 +1 < -1

4 < 0 (This is False)

Step 2  - Plug in (-1, 1) in to the second equation. where y = -1 and x = 1.

-1 < (3/2)(1) - 1

-1 < 1/2 (This is true).

Thus (-1, 1) is only partially included in the solution area.)

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