Determine the relationship between the point (1, –5) and the given system of inequalities.

y ≤ 3x + 2

y > –2x – 3

explain your answer both algebraically and graphically.

sample response: algebraically, the point (1, -5) satisfies the first inequality, but it does not satisfy the second inequality because -5 is not greater than -5. graphically, the point (1, -5) lies in the shaded area of the first inequality but lies on the dashed line of the second inequality, which is not inclusive. therefore (1, -5) is not a solution to the given system of inequalities.

Y ≤ 3x + 2

y > -2x - 3

At point (1, -5): -5 ≤ 3(1) + 2

-5 ≤ 5

-5 > -2(1) - 3

-5 > -2 - 3

-5 is not greater than -5.

Point (1, -5) is not a solution to the system of inequalities.

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Step-by-step explanation:

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Y < = 3x + 2...subbing in (1,-5)

-5 < = 3(1) + 2

-5 < = 3 + 2

-5 < = 5 (true)

y > -2x - 3...subbing in (1,-5)

-5 > -2(1) - 3

-5 > -2 - 3

-5 > -5 (false)

response : Algebraically, the point (1,-5) satisfies the first inequality, but does not satisfy the second inequality because -5 is not greater then -5.Graphically, the point (1,-5) lies in the shaded area of the first inequality but lies on the dashed line of the second inequality, which is not inclusive. Therefore, (1,5) is not a solution to the given system of inequalities.

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Step-by-step explanation:

The point is not a solution for both inequalities, so the point is not a solution for the system of inequalities.

Step-by-step explanation:

To find the relationship of the point and the system of inequalities, let's use the value of the point (x and y values) in the inequalities:

First inequality: y ≤ 3x + 2

Using x = 1 and y = -5, we have:

-5 ≤ 3*1 + 2

-5 ≤ 3 + 2

-5 ≤ 5 (True)

Second inequality: y > –2x – 3

Using x = 1 and y = -5, we have:

-5 > -2*1 - 3

-5 > -2 - 3

-5 > -5 (False)

The point is not a solution for both inequalities, so the point is not a solution for the system.

Graphically, the point is not inside the area generated by the system of inequalities (check the image attached).

[tex]Determine the relationship between the point (1, –5) and the given system of inequalities. y ≤ 3x +[/tex]

Algebraically, the point (1, -5) satisfies the first inequality, but it does not satisfy the second inequality because -5 is not greater than -5. Graphically, the point (1, -5) lies in the shaded area of the first inequality but lies on the dashed line of the second inequality, which is not inclusive. Therefore (1, -5) is not a solution to the given system of inequalities.

Algebraically, the point (1,-5) satisfies the first inequality, but does not satisfy the second inequality because -5 is not greater then -5.Graphically, the point (1,-5) lies in the shaded area of the first inequality but lies on the dashed line of the second inequality, which is not inclusive. Therefore, (1,5) is not a solution to the given system of inequalities.

Step-by-step explanation:

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