Question

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

Answer 1

c

Explanation:

Answer 2

`y > -3` and
`y \geq (2)/(3)x- 4`

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

`y < -3` ----> inequality A

`y \leq (2)/(3)x- 4` ----> inequality B

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

Inequality A

`-2< -3` ----> is not true

therefore

The ordered pair is not a solution of the system A

Case B) we have

`y > -3` ----> inequality A

`y \geq (2)/(3)x- 4` ----> inequality B

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

Inequality A

`-2< -3` ----> is true

Inequality B

`-2 \geq (2)/(3) (3)-4` ----> is true

therefore

The ordered pair is a solution of the system B

Case C) we have

`y< -3`----> inequality A

`y \geq (2)/(3)x- 4` ----> inequality B

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

Inequality A

`-2< -3` ----> is not true

therefore

The ordered pair is not a solution of the system C

Case D) we have

y > -2 ----> inequality A

`y \leq (2)/(3)x- 4` ----> inequality B

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

Inequality A

`-2> -2` ----> is not true

therefore

The ordered pair is not a solution of the system D