Directions: Compare the values of x and y using the information below.

I. $x={21}^2-{16}^2-5^3$
II. $(y+11)(y-11)=75$

The correct option is If x > y.

To compare the values of x and y, we need to solve both given equations step-by-step.

Step 1: Calculate the value of x from Equation I

The first equation is:

$x={21}^2-{16}^2-5^3$

Calculate each exponent term individually:

${21}^2=441$

${16}^2=256$

$5^3=125$

Substitute these values back into Equation I:

$x=441-256-125$

$x=441-381$

$x=60$

Step 2: Calculate the values of y from Equation II

The second equation is:

$(y+11)(y-11)=75$

Apply the difference of squares algebraic identity $(a+b)(a-b)=a^2-b^2$:

$y^2-{11}^2=75$

$y^2-121=75$

Add 121 to both sides to isolate $y^2$:

$y^2=75+121$

$y^2=196$

Take the square root of both sides:

$y=\pm 14$

Thus, $y$ has two possible values: $y=14$ or $y=-14$.

Step 3: Compare x and y

Compare $x=60$ with each possible value of $y$:

1. When $y=14$: $60>14$, so $x>y$.
2. When $y=-14$: $60>-14$, so $x>y$.

In both cases, $x$ is strictly greater than $y$. Therefore, the correct relationship is If x > y.