In the following questions, two equations numberded I and II are given. You have to solve both the equations and give answer If:
`I. 55x^2 -495x+1100=0 II. 5y^2+10y-120=0`

Options

A. `x lt y`
B. `x ge y`
C. `x gt y`
D. `x le y`

Answer

To solve the given equations, we will follow these steps:

### Step 1: Solve Equation I
The first equation is:
\[ 55x^2 - 495x + 1100 = 0 \]

**Hint:** Start by simplifying the equation by dividing all terms by a common factor.

We can divide the entire equation by 11:
\[ 5x^2 - 45x + 100 = 0 \]

**Hint:** Look for another common factor to simplify further.

Next, divide the equation by 5:
\[ x^2 - 9x + 20 = 0 \]

**Hint:** Now, factor the quadratic equation.

To factor \( x^2 - 9x + 20 \), we need two numbers that multiply to 20 and add to -9. The factors are -5 and -4:
\[ (x - 5)(x - 4) = 0 \]

**Hint:** Set each factor to zero to find the values of x.

Setting each factor to zero gives:
1. \( x - 5 = 0 \) → \( x = 5 \)
2. \( x - 4 = 0 \) → \( x = 4 \)

### Step 2: Solve Equation II
The second equation is:
\[ 5y^2 + 10y - 120 = 0 \]

**Hint:** Simplify this equation by dividing by a common factor.

We can divide the entire equation by 5:
\[ y^2 + 2y - 24 = 0 \]

**Hint:** Factor the quadratic equation.

To factor \( y^2 + 2y - 24 \), we need two numbers that multiply to -24 and add to 2. The factors are 6 and -4:
\[ (y + 6)(y - 4) = 0 \]

**Hint:** Set each factor to zero to find the values of y.

Setting each factor to zero gives:
1. \( y + 6 = 0 \) → \( y = -6 \)
2. \( y - 4 = 0 \) → \( y = 4 \)

### Step 3: Compare Values of x and y
Now we have:
- From Equation I: \( x = 4 \) or \( x = 5 \)
- From Equation II: \( y = 4 \) or \( y = -6 \)

**Hint:** Consider all combinations of x and y values.

1. If \( x = 4 \) and \( y = 4 \): \( x = y \)
2. If \( x = 4 \) and \( y = -6 \): \( x > y \)
3. If \( x = 5 \) and \( y = 4 \): \( x > y \)
4. If \( x = 5 \) and \( y = -6 \): \( x > y \)

### Conclusion
From these comparisons, we can conclude that:
- In all cases, \( x \) is greater than or equal to \( y \).

Thus, the final answer is:
\[ x \geq y \]

### Final Answer
The correct option is: \( x \) is greater than or equal to \( y \).

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