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(B) For equation $I$: $x^{2}-16x+63=0$We need two numbers whose product is $63$ and sum is $16$. These are $9$ and $7$.$x^{2}-9x-7x+63=0$$x(x-9)-7(x-9

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if $x \ge y$

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(B) For equation $I$: $x^{2}-16x+63=0$We need two numbers whose product is $63$ and sum is $16$. These are $9$ and $7$.$x^{2}-9x-7x+63=0$$x(x-9)-7(x-9)=0$$(x-9)(x-7)=0$So,$x = 9$ or $x = 7$.For equation $II$: $y^{2}-2y-35=0$We need two numbers whose product is $-35$ and sum is $-2$. These are $-7$ and $5$.$y^{2}-7y+5y-35=0$$y(y-7)+5(y-7)=0$$(y-7)(y+5)=0$So,$y = 7$ or $y = -5$.Comparing the values:If $x=9$,then $x > y$ (since $y$ is $7$ or $-5$).If $x=7$,then $x \ge y$ (since $y$ is $7$ or $-5$).Combining these,we get $x \ge y$.

Solve the given two equations and select the correct answer from the given options.
$I.$ $x^{2}-16x+63=0$
$II.$ $y^{2}-2y-35=0$

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Solve the given two equations and select the correct answer from the given options.$I.$ $x^{2}-16x+63=0$$II.$ $y^{2}-2y-35=0$