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inysia [295]
3 years ago
7

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

Mathematics
2 answers:
LiRa [457]3 years ago
7 0

<u>Answer:</u>

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

<u>Step-by-step explanation:</u>

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

y

y>x^2-4

A. (0, 8):

y ---> 8 - False

y>x^2-4 ---> 8>0^2-4 = 8 > -4 - True

B. (4, 2):

y ---> 2 - True

y>x^2-4 ---> 2>4^2-4 = 2> 12 - False

C. (2, 6):

y ---> 6 - True

y>x^2-4 ---> 6>2^2-4 = 6> 0 - True

D. (-2, -4):

y ---> -4 - True

y>x^2-4 ---> -4>(-2)^2-4 = -4> 0 - False

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

asambeis [7]3 years ago
5 0
<h2>Hello!</h2>

The answer is:

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

<h2>Why?</h2>

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

We are given the inequalities:

yx^{2}-4

Checking, we have:

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

First inequality,

y

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,

y

Second inequality,

y>x^{2}-4\\2>4^{2}-4\\2>16-4\\2>12

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,

y

Second inequality,

y>x^{2}-4\\6>2^{2}-4\\6>4-4\\6>0

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)

y

Second inequality,

y>x^{2}-4\\-4>2^{2}-4\\-4>4-4\\-4>0

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!

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