Directions (41-45): In each of these questions, two equations (I) and (II) are given. Solve the equations and mark the correct option.

I: 2x² + 10x + 12 = 0
II: y² + 10x + 25 = 0

The correct answer is If x > y.

To find the relationship between $x$ and $y$, we need to solve both given equations step-by-step.

Step 1: Solve Equation I for $x$

The first equation is:

$2x^2+10x+12=0$

Divide the entire equation by 2 to simplify:

$x^2+5x+6=0$

Factorize the quadratic equation by finding two numbers that multiply to 6 and add up to 5 (which are 2 and 3):

$(x+2)(x+3)=0$

Solving for $x$:

$x=-2$ or $x=-3$

Step 2: Solve Equation II for $y$

The second equation is:

$y^2+10y+25=0$

This is a perfect square quadratic equation:

$(y+5{)}^2=0$

Solving for $y$:

$y=-5$

Step 3: Compare the values of $x$ and $y$

Comparing the values of $x$ ($-2$ and $-3$) with $y$ ($-5$):

1. When $x=-2$ and $y=-5$, $-2>-5$ (so $x>y$).

2. When $x=-3$ and $y=-5$, $-3>-5$ (so $x>y$).

Therefore, in both cases, $x>y$.