The points were the systems are true in the white areas, the colored areas are the excluded ones.

You are watching: Which system of linear inequalities has the point (3, –2) in its solution set?

Now we need to put our point in both systems and see if the point is a solution or not,

In the first one, you can see that y needs to be less than -2, and in out point y is equal to 2, then the point (3,2) cant is a solution of the first system.

let"s see the second system:

Y > - 2

Y ≤ (2/3)x - 4

valuate it in the point (3,2)

2 > -2

2 ≤ (2/3)*3 - 4 = - 2

this is also false.

Then the point (3,2) is not a solution for neither system, and you can see it in the graphs, in the first graph the point (3,2) is in the black area, and in the second one is in the red area.

and

Step-by-step explanation:

The complete question is

Which system of linear inequalities has the point (3,-2) in its solution set?

A.

y -3

y ≥ 2/3x - 4

C.

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 B

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

Inequality A

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

Inequality B  ----> is true

therefore

The ordered pair is a solution of the system B

Case C) we have ----> inequality B

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

Inequality A

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

and

Step-by-step explanation:

The complete question is

Which system of linear inequalities has the point (3,-2) in its solution set?

y -3

y ≥ 2/3x - 4

C.

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 B

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

Inequality A

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

Inequality B ----> is true

therefore

The ordered pair is a solution of the system B

Case C) we have ----> inequality B

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

Inequality A

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