Question

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.

Answer 1

Answer:

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.

Step-by-step explanation:

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Answer 2

Answer:

In terms of algebra, the point (1, -5) fulfills the first inequality, but not the second, since -5 is not bigger than -5. The point (1, -5) on the graph is in the shaded region of the first inequality, but it is on the dashed line of the second inequality, which is not inclusive.