Select the point that is a solution to the system of inequalities

The answer is:

The point C. (2,6) is a solution to the system of inequalities.

To check what point is a solution to the system of inequalities, the point must satisfy both inequalities, so:

We are given the inequalities:

Checking, we have:

- Substituting A(0,8), we have:

First inequality,

Now, since 8 is not less than 6, we know that A (0,8) is not a solution to the system of inequalities since it does not satisfy both inequalities.

- Substituting B(4,2), we have:

First inequality,

Second inequality,

Now, since 2 is not greater than 12, we know that B(4,2) is not a solution to the system of inequalities since it does not satisfy both inequalities.

- Substituting C(2,6), we have:

First inequality,

Second inequality,

Now, as we can se, both inequalities are satisfied since 6 is less than 10 and greater than 0, so C(2,6) is a solution to the system.

- Substituting D(-2,-4)

Second inequality,

Now, since -4 is not greater than 0, we know that D(-2,-4) is not a solution to the system of inequalities since it does not satisfy both inequalities.

Hence,

Only the point C. (2,6) is a solution to the system of inequalities.

Have a nice day!

The correct answer option is C. (2, 6).

Step-by-step explanation:

We are given the following inequalities so we will check each point if it satisfies them:

A. (0, 8):

---> - False

---> - True

B. (4, 2):

---> - True

---> - False

C. (2, 6):

---> - True

---> - True

D. (-2, -4):

---> - True

---> - False

Therefore, the point which is the solution to this system of inequalities is C. (2, 6).