In each question, two equations numbered I and II have been given. you have to solve both the equations and mark the appropiate option.
I `10x^2+21x+8=0`
II `5y^2+19y+18=0`

Options

A. `xley`
B. `xgey`
C. `xlty`
D. `xgty`

Answer

To solve the equations given in the question step by step, we will tackle each equation separately.

### Step 1: Solve Equation I
The first equation is:
\[ 10x^2 + 21x + 8 = 0 \]

To factor this quadratic equation, we need to express the middle term (21x) as a sum of two terms whose coefficients multiply to \(10 \times 8 = 80\) and add up to \(21\).

We can split \(21x\) into \(16x + 5x\):
\[ 10x^2 + 16x + 5x + 8 = 0 \]

Now we can group the terms:
\[ (10x^2 + 16x) + (5x + 8) = 0 \]

Factoring out the common terms:
\[ 2x(5x + 8) + 1(5x + 8) = 0 \]

Now we can factor by grouping:
\[ (2x + 1)(5x + 8) = 0 \]

Setting each factor to zero gives us:
1. \(2x + 1 = 0 \Rightarrow x = -\frac{1}{2}\)
2. \(5x + 8 = 0 \Rightarrow x = -\frac{8}{5}\)

Thus, the solutions for \(x\) are:
\[ x = -\frac{1}{2}, -\frac{8}{5} \]

### Step 2: Solve Equation II
The second equation is:
\[ 5y^2 + 19y + 18 = 0 \]

Similarly, we need to express \(19y\) as a sum of two terms whose coefficients multiply to \(5 \times 18 = 90\) and add up to \(19\).

We can split \(19y\) into \(10y + 9y\):
\[ 5y^2 + 10y + 9y + 18 = 0 \]

Now we can group the terms:
\[ (5y^2 + 10y) + (9y + 18) = 0 \]

Factoring out the common terms:
\[ 5y(y + 2) + 9(y + 2) = 0 \]

Now we can factor by grouping:
\[ (5y + 9)(y + 2) = 0 \]

Setting each factor to zero gives us:
1. \(5y + 9 = 0 \Rightarrow y = -\frac{9}{5}\)
2. \(y + 2 = 0 \Rightarrow y = -2\)

Thus, the solutions for \(y\) are:
\[ y = -2, -\frac{9}{5} \]

### Step 3: Compare the Solutions
Now we have the solutions:
- For \(x\): \(x = -\frac{1}{2}, -\frac{8}{5}\)
- For \(y\): \(y = -2, -\frac{9}{5}\)

Next, we will compare the values of \(x\) and \(y\):
- The largest value of \(x\) is \(-\frac{1}{2}\) and the largest value of \(y\) is \(-2\).

Since \(-\frac{1}{2} > -2\), we conclude that:
\[ x > y \]

### Final Answer
The appropriate option is:
\[ x > y \]