In each question, two equations numbered I and II are given. You have to solve both the equations and mark the appropriate answers
I `2x^2-15x+28=0`
II `y^2-7y+12=0`

Options

A. `xley`
B. `xlty`
C. `xgey`
D. x=y or relationship between x and y can’t be established

Answer

To solve the given equations step by step, we will follow the quadratic formula and factorization method.

### Step 1: Solve the first equation \(2x^2 - 15x + 28 = 0\)

1. **Identify the coefficients**:
- \(a = 2\), \(b = -15\), \(c = 28\)

2. **Factor the quadratic equation**:
We need to find two numbers that multiply to \(a \cdot c = 2 \cdot 28 = 56\) and add to \(b = -15\).
- The numbers that satisfy this are \(-7\) and \(-8\).

3. **Rewrite the equation**:
\[ 2x^2 - 7x - 8x + 28 = 0 \]

4. **Group the terms**:
\[ (2x^2 - 7x) + (-8x + 28) = 0 \]

5. **Factor by grouping**:
\[ x(2x - 7) - 4(2x - 7) = 0 \]
\[ (2x - 7)(x - 4) = 0 \]

6. **Set each factor to zero**:
- \(2x - 7 = 0 \Rightarrow x = \frac{7}{2} = 3.5\)
- \(x - 4 = 0 \Rightarrow x = 4\)

### Step 2: Solve the second equation \(y^2 - 7y + 12 = 0\)

1. **Identify the coefficients**:
- \(a = 1\), \(b = -7\), \(c = 12\)

2. **Factor the quadratic equation**:
We need to find two numbers that multiply to \(c = 12\) and add to \(b = -7\).
- The numbers that satisfy this are \(-3\) and \(-4\).

3. **Rewrite the equation**:
\[ y^2 - 3y - 4y + 12 = 0 \]

4. **Group the terms**:
\[ (y^2 - 3y) + (-4y + 12) = 0 \]

5. **Factor by grouping**:
\[ y(y - 3) - 4(y - 3) = 0 \]
\[ (y - 3)(y - 4) = 0 \]

6. **Set each factor to zero**:
- \(y - 3 = 0 \Rightarrow y = 3\)
- \(y - 4 = 0 \Rightarrow y = 4\)

### Step 3: Compare the values of \(x\) and \(y\)

- From the first equation, we have \(x = 3.5\) and \(x = 4\).
- From the second equation, we have \(y = 3\) and \(y = 4\).

### Conclusion

- The possible values for \(x\) are \(3.5\) and \(4\).
- The possible values for \(y\) are \(3\) and \(4\).
- Comparing the values:
- When \(x = 3.5\), \(y = 3\) → \(x > y\)
- When \(x = 4\), \(y = 4\) → \(x = y\)

Thus, the relationship between \(x\) and \(y\) is \(x \geq y\).

### Final Answer
The correct answer is \(x \geq y\).

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