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.
Answers
Given : y ≤ 3x + 2
y > –2x – 3
To Find : Determine the relationship between the point (1, –5) and the given system of inequalities.
Solution:
y ≤ 3x + 2
x = 1
=> y ≤ 3(1) + 2
=> y ≤ 5
- 5 ≤ 5
Hence point (1, –5) satisfy y ≤ 3x + 2
Graph is drawn
y > –2x – 3
x = 1
=> y > -2(1) - 3
=> y > - 5
but - 5 = -5
Hence point (1, –5) does not satisfy y > –2x – 3
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Answer: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: this is the sample response:)