Directions (31-35): In each of the following questions two equations are given. Solve these equations and give answer:

I. x² + 12x + 35 = 0
II. y² + 9y + 20 = 0

To determine the relationship between $x$ and $y$, we need to solve the two given quadratic equations.

Step 1: Solve Equation I for $x$
The first equation is given by:
$x^2+12x+35=0$

We can solve this quadratic equation by factoring. We need to find two numbers that multiply to 35 and add up to 12. These numbers are 7 and 5.
$x^2+7x+5x+35=0$
$x(x+7)+5(x+7)=0$
$(x+7)(x+5)=0$

This gives the roots:
$x=-7$ or $x=-5$

Step 2: Solve Equation II for $y$
The second equation is given by:
$y^2+9y+20=0$

Similarly, we factor this equation by finding two numbers that multiply to 20 and add up to 9. These numbers are 5 and 4.
$y^2+5y+4y+20=0$
$y(y+5)+4(y+5)=0$
$(y+5)(y+4)=0$

This gives the roots:
$y=-5$ or $y=-4$

Step 3: Compare the values of $x$ and $y$
Let us compare each value of $x$ with each value of $y$:
- For $x=-7$:
  Comparing with $y=-5$, we have $-7<-5$ (i.e., $x<y$).
  Comparing with $y=-4$, we have $-7<-4$ (i.e., $x<y$).
- For $x=-5$:
  Comparing with $y=-5$, we have $-5=-5$ (i.e., $x=y$).
  Comparing with $y=-4$, we have $-5<-4$ (i.e., $x<y$).

Combining all the comparisons, we get that in all cases, $x\le y$.

Thus, the correct option is if x ≤ y.