Which graph represents the solution set of the system of inequalities? {y< −3x−2y y≤x−2

The graph that represents the solution to the system of inequalities is graph (a).

The system of inequalities is given as:

The above highlights means that the shaded region that represent the solution to the system of inequalities will be at the left-hand side

Hence, graph (a) represents the system of inequalities

Read more about system of inequalities at:

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Option 1

Step-by-step explanation:

In each inequality we have the equation of a line.

The first step in solving this problem is to identify each line in the figures.

To do this, we willient your cut points.

y = x-2

We do y = 0

0 = x-2

x = 2. This line cuts the x-axis at x = 2.

Now we do x = 0

y = -2.

This line cuts the y-axis in y = -2.

Now we can identify this line in the figure.

The inequality is:

y≤x - 2

Then the region that represents this inequality are all the points below the line y = x-2 and also those that belong to the line.

Try for example the point (0, -4) that is below this line.

-4≤0-2

-4≤-2. The inequality is met.

We do the same for the other line:

y<-3x - 2

y = -3x-2.

The cut points are:

2 = -3x

x = -2 / 3

y = -2

Locate in the graphs the line that meets these characteristics.

The region understood by this inequality are all points below the line

y = -3x-2 and which, in turn, are below the line y = x-2.

Once again, the point (-4.0) complies with both inequalities.

Identify these characteristics in the options, and you will see that the correct option is the first

step-by-step explanation: