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

y less-than negative 3. y less-than-or-equal-to two-thirds x minus 4 on a coordinate plane, 2 straight lines are shown. the first dashed line is horizontal to the y-axis at y = negative 3. everything below the line is shaded. the second solid line has a positive slope and goes through (0, negative 4) and (3, negative 2). everything below the line is shaded.
y greater-than negative 3. y greater-than-or-equal-to two-thirds x minus 4 on a coordinate plane, 2 straight lines are shown. the first dashed line is horizontal to the y-axis at y = negative 3. everything above the line is shaded. the second solid line has a positive slope and goes through (0, negative 4) and (3, negative 2). everything above the line is shaded.
y less-than negative 3. y greater-than-or-equal-to two-thirds x minus 4 on a coordinate plane, 2 straight lines are shown. the first dashed line is horizontal to the y-axis at y = negative 3. everything below the line is shaded. the second solid line has a positive slope and goes through (0, negative 4) and (3, negative 2). everything above the line is shaded.
y greater-than negative 2. y less-than-or-equal-to two-thirds x minus 4

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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

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

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

i hope this you!