Determine whether the point (3,3) is in the solution set of the system of inequalities below. y ≤ –x – 2

y ≥ –5x + 2

      The ordered pair is not a solution of the system D

explanation:

A.

y < -3

y ≤ 2/3x - 4

B.

y > -3

y ≥ 2/3x - 4

C.

y < -3

y ≥ 2/3x - 4

D.

y > -2

y ≤ 2/3x - 4

we know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities (makes true both inequalities)

Verify each case

Case A) we have

> inequality A

> inequality B

Substitute the value of x and  y of the point (3,-2) in both inequalities and then compare the results

Inequality A

> is not true

therefore

The ordered pair is not a solution of the system A

Case B) we have

> inequality A

> inequality B

Substitute the value of x and  y of the point (3,-2) in both inequalities and then compare the results

Inequality A

> is true

Inequality B

> is true

therefore

The ordered pair is a solution of the system B

Case C) we have

> inequality A

> inequality B

Substitute the value of x and  y of the point (3,-2) in both inequalities and then compare the results

Inequality A

 > is not true

therefore

The ordered pair is not a solution of the system C

Case D) we have

y > -2 > inequality A

> inequality B

Substitute the value of x and y of the point (3,-2) in both inequalities and then compare the results

Inequality A

> is not true

therefore

The ordered pair is not a solution of the system D

-1/4 > -1 2/3. -1/4 is greater than -1 2/3 because it is closer to 0 on the number line.