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 On a coordinate plane, 2 straight lines are shown. The first dashed line is horizontal at y = negative 2. 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 below the line is shaded.

Answer 1

Answer:

$y > -3$  and  $y \geq \frac{2}{3}x- 4$

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

$y < -3$ ----> inequality A

$y \leq \frac{2}{3}x- 4$ ----> 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

$y \geq \frac{2}{3}x- 4$ ----> 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

$-2 \geq \frac{2}{3} (3)-4$

$-2\geq -2$ ----> is true

therefore

The ordered pair is a solution of the system B

Case C) we have

$y< -3$----> inequality A

$y \geq \frac{2}{3}x- 4$ ----> 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

$y \leq \frac{2}{3}x- 4$ ----> 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