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Which ordered pair is in the inverse of the relation given by x?y+7y=64?

A) (2, 10)
B) (5, 6)
C) (8, 9)
D) (7, 8)

1 Answer

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Final answer:

To find the inverse of the relation, solve for y in terms of x. Check each option by substituting x and y values into the inverse equation. None of the given options is in the inverse relation.

Step-by-step explanation:

To find the inverse of a relation, we need to solve for y in terms of x. In the given relation, x + y + 7y = 64, combine like terms to get x + 8y = 64. Now, solve for y by isolating it on one side of the equation. Subtract x from both sides to get 8y = 64 - x. Divide both sides by 8 to get y = (64 - x) / 8. This is the equation for the inverse relation. Now we can check which ordered pair is in the inverse relation by substituting the x and y values of each option into the equation and see if they satisfy it.

Checking option A: (2, 10). Substituting x = 2 and y = 10 into the equation gives y = (64 - 2) / 8 = 62 / 8 = 7.75, not equal to 10. So, option A is not in the inverse relation.

Checking option B: (5, 6). Substituting x = 5 and y = 6 into the equation gives y = (64 - 5) / 8 = 59 / 8 = 7.375, not equal to 6. So, option B is not in the inverse relation.

Checking option C: (8, 9). Substituting x = 8 and y = 9 into the equation gives y = (64 - 8) / 8 = 56 / 8 = 7, not equal to 9. So, option C is not in the inverse relation.

Checking option D: (7, 8). Substituting x = 7 and y = 8 into the equation gives y = (64 - 7) / 8 = 57 / 8 = 7.125, not equal to 8. So, option D is not in the inverse relation.

None of the given options is in the inverse relation. Therefore, the correct answer is none of the given options.

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