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(C) For equation $I$: $35x^{2} - 53x + 20 = 0$We factorize the quadratic equation: $35x^{2} - 28x - 25x + 20 = 0$$7x(5x - 4) - 5(5x - 4) = 0$$(7x - 5)

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$x < y$

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(C) For equation $I$: $35x^{2} - 53x + 20 = 0$We factorize the quadratic equation: $35x^{2} - 28x - 25x + 20 = 0$$7x(5x - 4) - 5(5x - 4) = 0$$(7x - 5)(5x - 4) = 0$Thus,$x = \frac{5}{7} \approx 0.714$ or $x = \frac{4}{5} = 0.8$.For equation $II$: $56y^{2} - 97y + 42 = 0$We factorize the quadratic equation: $56y^{2} - 49y - 48y + 42 = 0$$7y(8y - 7) - 6(8y - 7) = 0$$(7y - 6)(8y - 7) = 0$Thus,$y = \frac{6}{7} \approx 0.857$ or $y = \frac{7}{8} = 0.875$.Comparing the values:$x$ values are ${0.714, 0.8}$ and $y$ values are ${0.857, 0.875}$.Since all values of $x$ are less than all values of $y$,we conclude that $x < y$.

Solve the given two equations and select the correct answer from the given options.
$I.$ $35x^{2} - 53x + 20 = 0$
$II.$ $56y^{2} - 97y + 42 = 0$

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Solve the given two equations and select the correct answer from the given options.$I.$ $35x^{2} - 53x + 20 = 0$$II.$ $56y^{2} - 97y + 42 = 0$