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(D) For equation $I$: $6x^2 + 77x + 121 = 0$Splitting the middle term: $6x^2 + 66x + 11x + 121 = 0$$6x(x + 11) + 11(x + 11) = 0$$(6x + 11)(x + 11) = 0

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If $x \leq y$ or no relationship can be established between $x$ and $y$

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(D) For equation $I$: $6x^2 + 77x + 121 = 0$Splitting the middle term: $6x^2 + 66x + 11x + 121 = 0$$6x(x + 11) + 11(x + 11) = 0$$(6x + 11)(x + 11) = 0$So,$x = -\frac{11}{6} \approx -1.83$ and $x = -11$.For equation $II$: $y^2 + 9y - 22 = 0$Splitting the middle term: $y^2 + 11y - 2y - 22 = 0$$y(y + 11) - 2(y + 11) = 0$$(y - 2)(y + 11) = 0$So,$y = 2$ and $y = -11$.Comparing the values:When $x = -1.83$,$x > y$ (since $y = -11$) and $x When $x = -11$,$x = y$ (since $y = -11$) and $x Since the relationship changes depending on the values chosen,no definite relationship can be established between $x$ and $y$.

Solve the given two equations and select the correct answer from the given options.
$I.$ $6x^2 + 77x + 121 = 0$
$II.$ $y^2 + 9y - 22 = 0$

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Solve the given two equations and select the correct answer from the given options.$I.$ $6x^2 + 77x + 121 = 0$$II.$ $y^2 + 9y - 22 = 0$