Question

Which region labeled in the graph below would represent the solution (the final shaded area) to the system of linear inequalities: y≤1/2x−3 y<−2/3x+1 Group of answer choices Region C, Region D, Region A, Region B

Answer 1

Region D.

Explanation:

Here we have two inequalities:

y ≤ 1/2x − 3

y < −2/3x + 1

First, we can see that the first inequality has a positive slope and the symbol (≤) so the values of the line itself are solutions, this line is the solid line in the graph.

And we have that:

y ≤ 1/2x − 3

y must be smaller or equal than the solid line, so here we look at the regions below the solid line, which are region D and region C.

Now let's look at the other one:

y < −2/3x + 1

y = (-2/3)*x + 1

is the dashed line in the graph.

And we have:

y < −2/3x + 1

So y is smaller than the values of the line, so we need to look at the region that is below de dashed line.

The regions below the dashed line are region A and region D.

The solution for the system:

y ≤ 1/2x − 3

y < −2/3x + 1

Is the region that is a solution for both inequalities, we can see that the only region that is a solution for both of them is region D.

Then the correct option is region D.