` 4x+2y = 8.5, 2x + 4y = 9.5`

Options

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

Explanation

To solve the system of equations given by:

1) \( 4x + 2y = 8.5 \)
2) \( 2x + 4y = 9.5 \)

we will follow these steps:

### Step 1: Simplify the equations
Let's simplify the second equation by multiplying it by 2 to make the coefficients of \(x\) in both equations the same.

\[ 2(2x + 4y) = 2(9.5) \]

This gives us:

\[ 4x + 8y = 19 \]

Now we have the two equations:

1) \( 4x + 2y = 8.5 \)
2) \( 4x + 8y = 19 \)

### Step 2: Subtract the first equation from the second
Now, we will subtract the first equation from the second equation to eliminate \(4x\):

\[ (4x + 8y) - (4x + 2y) = 19 - 8.5 \]

This simplifies to:

\[ 6y = 10.5 \]

### Step 3: Solve for \(y\)
Now, we can solve for \(y\) by dividing both sides by 6:

\[ y = \frac{10.5}{6} = 1.75 \]

### Step 4: Substitute \(y\) back into one of the original equations
Now that we have \(y\), we can substitute it back into the first equation to find \(x\):

\[ 4x + 2(1.75) = 8.5 \]

This simplifies to:

\[ 4x + 3.5 = 8.5 \]

### Step 5: Solve for \(x\)
Now, we will isolate \(x\):

\[ 4x = 8.5 - 3.5 \]
\[ 4x = 5 \]
\[ x = \frac{5}{4} = 1.25 \]

### Final Solution
The solution to the system of equations is:
\[ x = 1.25, \quad y = 1.75 \]