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PLEASE HELP. MATH IN PICTURE

PLEASE HELP. MATH IN PICTURE-example-1
User Joshweir
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Answer:

D . . . (best of the erroneous choices)

Explanation:

Solving the first equation for x, we get ...

√(y -1) ≥ x

Solving the second equation for x, we get ...

x > 3

Substituting for x, we have ...

√(y -1) > 3

y -1 > 9

y > 10

Ordered pairs that are in the solution set will have coordinates ...

x > 3, y > 10

In interval notation that looks like ...

x ∈ (-∞, 3) and y ∈ (10, ∞)

The closest answer choice is the last one.

_____

You will note that x must be strictly greater than 3, so y cannot be equal to 10. The offered choice is in error on that point.

__

You will also note that y is dependent on x. That is, one cannot pick a value of y greater than 10 independently of the value of x. In that sense, the solution is not "the set of all ordered pairs such that [x and y have independent limits]". Rather, it is the set of all ordered pairs such that √(y -1) ≥ x > 3.

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