I. ` 2x-3y=- 3.5`
IIgt ` 3x-2y =- 6.5`

Options

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

Explanation

To solve the system of equations:

1. **Equations Given:**
\[ \text{I. } 2x - 3y = -3.5 \quad \text{(Equation 1)} \]
\[ \text{II. } 3x - 2y = -6.5 \quad \text{(Equation 2)} \]

2. **Multiply the equations to align the coefficients of \(y\):**
- Multiply Equation 1 by 2:
\[ 2(2x - 3y) = 2(-3.5) \implies 4x - 6y = -7 \quad \text{(Equation 3)} \]
- Multiply Equation 2 by 3:
\[ 3(3x - 2y) = 3(-6.5) \implies 9x - 6y = -19.5 \quad \text{(Equation 4)} \]

3. **Set up the new system of equations:**
\[ \text{III. } 4x - 6y = -7 \quad \text{(Equation 3)} \]
\[ \text{IV. } 9x - 6y = -19.5 \quad \text{(Equation 4)} \]

4. **Subtract Equation 3 from Equation 4:**
\[ (9x - 6y) - (4x - 6y) = -19.5 - (-7) \]
\[ 9x - 4x = -19.5 + 7 \]
\[ 5x = -12.5 \]

5. **Solve for \(x\):**
\[ x = \frac{-12.5}{5} = -2.5 \]

6. **Substitute \(x\) back into one of the original equations to find \(y\):**
- Using Equation 1:
\[ 2(-2.5) - 3y = -3.5 \]
\[ -5 - 3y = -3.5 \]
\[ -3y = -3.5 + 5 \]
\[ -3y = 1.5 \]
\[ y = \frac{1.5}{-3} = -0.5 \]

7. **Final values:**
\[ x = -2.5, \quad y = -0.5 \]

8. **Determine the relationship between \(x\) and \(y\):**
\[ x < y \quad \text{(since } -2.5 < -0.5\text{)} \]