Directions: In the given question, two equations numbered I and II are provided. Solve both equations and establish the correct relationship between x and y.

I: $x^2-25x+150=0$
II: $y^2-7y+10=0$

The correct option is If x > y.

Solving Equation I:

$x^2-25x+150=0$

We look for two numbers whose product is 150 and sum is -25. These numbers are -15 and -10.

$x^2-15x-10x+150=0$

$x(x-15)-10(x-15)=0$

$(x-15)(x-10)=0$

Therefore, the values of x are:

$x=15$ or $x=10$

Solving Equation II:

$y^2-7y+10=0$

We look for two numbers whose product is 10 and sum is -7. These numbers are -5 and -2.

$y^2-5y-2y+10=0$

$y(y-5)-2(y-5)=0$

$(y-5)(\mathrm{y<mo>-</mo><mn>2</mn><mo>)</mo><mo>=</mo><mn>0</mn>}$

Therefore, the values of y are:

$y=5$ or $y=2$

Comparing x and y:

Comparing each value of x with each value of y:

When $x=15$: 15 > 5 and 15 > 2 (so $x>y$).

When $x=10$: 10 > 5 and 10 > 2 (so $x>y$).

In all cases, every value of x is strictly greater than every value of y. Hence, the correct relationship is $x>y$.