Identify the graph and describe the solution set of this system of inequalities.
y<-3x-2
y> -3x+ 8

We have the system:

y < -3*x - 2

y > -3*x + 8

The solution set of this system will be the intersection between the solution sets of both inequalities.

First, to find each set of solutions, we need to find the line:

y = -3*x - 2

Because we have the symbol <, the solution set will be all the points below this line, and the line will be a dashed line (meaning that the points on the line are not solutions).

For the other line we have the same approach.

First we need to find the line:

y = -3*x + 8

Now because we used the symbol >, we need to shade the region above the line, and again the line must be a shaded line.

The graph of this system can be seen below.

Where we can see that there is no intersection of the two solution sets, meaning that the system of inequalities has no solutions.

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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