PLEASE HELP. MATH IN PICTURE

9514 1404 393

  D . . . (best of the erroneous choices)

Step-by-step 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.