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(D) For equation $I$: $10 x^{2}-7 x+1=0$Splitting the middle term: $10 x^{2}-5 x-2 x+1=0$$5 x(2 x-1)-1(2 x-1)=0$$(5 x-1)(2 x-1)=0$So,$x = \frac{1}{5}

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If $x \geq y$

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(D) For equation $I$: $10 x^{2}-7 x+1=0$Splitting the middle term: $10 x^{2}-5 x-2 x+1=0$$5 x(2 x-1)-1(2 x-1)=0$$(5 x-1)(2 x-1)=0$So,$x = \frac{1}{5} = 0.2$ and $x = \frac{1}{2} = 0.5$.For equation $II$: $35 y^{2}-12 y+1=0$Splitting the middle term: $35 y^{2}-7 y-5 y+1=0$$7 y(5 y-1)-1(5 y-1)=0$$(7 y-1)(5 y-1)=0$So,$y = \frac{1}{7} \approx 0.143$ and $y = \frac{1}{5} = 0.2$.Comparing the values:$x$ values are ${0.2, 0.5}$ and $y$ values are ${0.143, 0.2}$.Since $0.2 \geq 0.143$,$0.2 = 0.2$,$0.5 > 0.143$,and $0.5 > 0.2$,we conclude that $x \geq y$.

Solve the given two equations and select the correct answer from the given options.
$I.$ $10 x^{2}-7 x+1=0$
$II.$ $35 y^{2}-12 y+1=0$

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Solve the given two equations and select the correct answer from the given options.$I.$ $10 x^{2}-7 x+1=0$$II.$ $35 y^{2}-12 y+1=0$