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Which coordinate pair is in the solution set for y < 1 - 6x?

A) (1, 0)
B) (1, -1)
C) (0, 1)
D) (-1, 1)

User Obmarg
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1 Answer

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Final answer:

To find which coordinate pair satisfies the inequality y < 1 - 6x, each pair must be tested by substituting the values into the inequality. Both options A (1, 0) and D (-1, 1) make the inequality true, but option A is the most straightforward choice since it has a y-value of 0, which is less than 1 and doesn't reach the maximum limit posed by the inequality.

Step-by-step explanation:

The student's question seeks to identify which coordinate pair satisfies the inequality y < 1 - 6x. To determine if a coordinate pair is part of the solution set for this inequality, we must substitute the x and y values from each option into the inequality and check if the inequality holds true.

  • For option A ((1, 0)), when we substitute x with 1 and y with 0, we get 0 < 1 - 6(1) or 0 < -5, which is true.
  • For option B ((1, -1)), substituting x with 1 and y with -1, we get -1 < 1 - 6(1) or -1 < -5, which is false.
  • For option C ((0, 1)), substituting x with 0 and y with 1, we get 1 < 1 - 6(0) or 1 < 1, which is false.
  • For option D ((-1, 1)), substituting x with -1 and y with 1, we get 1 < 1 - 6(-1) or 1 < 7, which is true.

Out of these options, both A and D satisfy the inequality y < 1 - 6x, but the question asks for which one is in the solution set. Since the question suggests a single answer and option D provides a y-value that is the maximum allowable (since y must be less than 1), option A, which has a y-value of 0, is the preferable choice.

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