Directions: Solve the two given equations and select the correct option to describe the relationship between x and y.

$\text{I.}{x}^3+29=758$

$\text{II.}{y}^2-81=0$

The correct option is x ≥ y.

Step 1: Solve Equation I for x

The first equation is:
$x^3+29=758$
Subtract 29 from both sides:
$x^3=758-29$
$x^3=729$
Take the cube root of both sides:
$x=\sqrt[3]{729}$
$x=9$

Step 2: Solve Equation II for y

The second equation is:
$y^2-81=0$
Add 81 to both sides:
$y^2=81$
Take the square root of both sides (yielding both positive and negative values):
$y=\pm \sqrt{81}$
$y=9\text{or}y=-9$

Step 3: Compare the values of x and y

Now, compare each value of $x$ with each value of $y$:
1. When $x=9$ and $y=9$, we have $x=y$.
2. When $x=9$ and $y=-9$, we have $x>y$.
Combining both scenarios yields:
$x\ge y$