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(C) For equation $I$: $x^{2}+5x+6=0$Factoring the quadratic: $x^{2}+3x+2x+6=0$$x(x+3)+2(x+3)=0$$(x+2)(x+3)=0$So,$x = -2$ or $x = -3$.For equation $II$

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if $x \ge y$

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(C) For equation $I$: $x^{2}+5x+6=0$Factoring the quadratic: $x^{2}+3x+2x+6=0$$x(x+3)+2(x+3)=0$$(x+2)(x+3)=0$So,$x = -2$ or $x = -3$.For equation $II$: $y^{2}+7y+12=0$Factoring the quadratic: $y^{2}+4y+3y+12=0$$y(y+4)+3(y+4)=0$$(y+3)(y+4)=0$So,$y = -3$ or $y = -4$.Comparing the values:If $x = -2$,then $x > y$ (since $-2 > -3$ and $-2 > -4$).If $x = -3$,then $x \ge y$ (since $-3 = -3$ and $-3 > -4$).Combining these,we get $x \ge y$.

Solve the given two equations and select the correct answer from the given options.
$I.$ $x^{2}+5x+6=0$
$II.$ $y^{2}+7y+12=0$

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Solve the given two equations and select the correct answer from the given options.$I.$ $x^{2}+5x+6=0$$II.$ $y^{2}+7y+12=0$