In each of the following questions, two equations are given. You have to solve them and
I. `x=(5)/(4)y`
`(y)/(2)=(-9)/(4)`

Options

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

Answer

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

### Step 1: Write down the equations
We have two equations:
1. \( x = \frac{5}{4}y \)
2. \( \frac{y}{2} = -\frac{9}{4} \)

### Step 2: Solve the second equation for \( y \)
To find the value of \( y \), we can multiply both sides of the second equation by 2:
\[ y = 2 \times -\frac{9}{4} \]
Calculating this gives:
\[ y = -\frac{18}{4} = -\frac{9}{2} \]

### Step 3: Substitute \( y \) into the first equation to find \( x \)
Now that we have \( y \), we can substitute it into the first equation:
\[ x = \frac{5}{4} \left(-\frac{9}{2}\right) \]
Calculating this gives:
\[ x = -\frac{45}{8} \]

### Step 4: Convert the values of \( x \) and \( y \) to decimal form
Now, let's convert \( y \) and \( x \) into decimal form for easier comparison:
- For \( y = -\frac{9}{2} \):
\[ y = -4.5 \]
- For \( x = -\frac{45}{8} \):
\[ x = -5.625 \]

### Step 5: Compare the values of \( x \) and \( y \)
Now we need to compare \( x \) and \( y \):
- \( x = -5.625 \)
- \( y = -4.5 \)

Since \(-5.625\) is less than \(-4.5\), we can conclude:
\[ x < y \]

### Final Conclusion
Thus, the relationship between \( x \) and \( y \) is:
\[ x \text{ is less than } y \]