In the following questions two equations numbered I and II are given. Solve both the equations and give answer
I. `x^2+6x-16=0` II. `y^2-6y+5=0`

Options

A. `xgey`
B. `xlty`
C. `xley`
D. relationship can't be established

Answer

To solve the given equations step by step, we will follow the standard method for solving quadratic equations.

### Step 1: Solve Equation I: \( x^2 + 6x - 16 = 0 \)

1. **Identify the coefficients**: Here, \( a = 1 \), \( b = 6 \), and \( c = -16 \).
2. **Use the quadratic formula**: The quadratic formula is given by:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
3. **Calculate the discriminant**:
\[ b^2 - 4ac = 6^2 - 4 \cdot 1 \cdot (-16) = 36 + 64 = 100 \]
4. **Calculate the roots**:
\[ x = \frac{-6 \pm \sqrt{100}}{2 \cdot 1} = \frac{-6 \pm 10}{2} \]
- For \( x_1 \):
\[ x_1 = \frac{-6 + 10}{2} = \frac{4}{2} = 2 \]
- For \( x_2 \):
\[ x_2 = \frac{-6 - 10}{2} = \frac{-16}{2} = -8 \]
5. **Roots of Equation I**: \( x = 2 \) and \( x = -8 \).

### Step 2: Solve Equation II: \( y^2 - 6y + 5 = 0 \)

1. **Identify the coefficients**: Here, \( a = 1 \), \( b = -6 \), and \( c = 5 \).
2. **Use the quadratic formula**:
\[ y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
3. **Calculate the discriminant**:
\[ b^2 - 4ac = (-6)^2 - 4 \cdot 1 \cdot 5 = 36 - 20 = 16 \]
4. **Calculate the roots**:
\[ y = \frac{6 \pm \sqrt{16}}{2 \cdot 1} = \frac{6 \pm 4}{2} \]
- For \( y_1 \):
\[ y_1 = \frac{6 + 4}{2} = \frac{10}{2} = 5 \]
- For \( y_2 \):
\[ y_2 = \frac{6 - 4}{2} = \frac{2}{2} = 1 \]
5. **Roots of Equation II**: \( y = 5 \) and \( y = 1 \).

### Step 3: Analyze the relationships between the roots

- From Equation I, we found \( x = 2 \) and \( x = -8 \).
- From Equation II, we found \( y = 5 \) and \( y = 1 \).

Now we can compare the values:
- \( y = 5 \) is greater than both \( x = 2 \) and \( x = -8 \).
- \( y = 1 \) is greater than \( x = -8 \) but less than \( x = 2 \).

### Conclusion:
Since there is no consistent relationship that can be established between \( x \) and \( y \) (as one value of \( y \) is greater than both values of \( x \), while the other is less than one and greater than the other), we conclude that there is **no relationship** between \( x \) and \( y \).

### Final Answer:
The correct option is **no relationship**.