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(D) Step $1$: Solve for $x$.$x = \sqrt[3]{2197} = 13$.Step $2$: Solve the quadratic equation for $y$.$2y^2 - 54y + 364 = 0$.Divide the entire equation

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if $x \le y$

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(D) Step $1$: Solve for $x$.$x = \sqrt[3]{2197} = 13$.Step $2$: Solve the quadratic equation for $y$.$2y^2 - 54y + 364 = 0$.Divide the entire equation by $2$:$y^2 - 27y + 182 = 0$.We need two numbers that multiply to $182$ and add to $-27$. These numbers are $-13$ and $-14$.$(y - 13)(y - 14) = 0$.Therefore,$y = 13$ or $y = 14$.Step $3$: Compare $x$ and $y$.$x = 13$.$y = 13$ or $14$.Comparing the values,$x = 13$ and $y = 13$ or $14$. In both cases,$x \le y$ is satisfied.Thus,the correct option is $D$.

Solve the given two equations and select the correct answer from the given options.
$I.$ $x = \sqrt[3]{2197}$
$II.$ $2y^2 - 54y + 364 = 0$

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Solve the given two equations and select the correct answer from the given options.$I.$ $x = \sqrt[3]{2197}$$II.$ $2y^2 - 54y + 364 = 0$