I. ` (3x-2)//y=(3x+6)//(y+16)`
II.` (x+2)//(y+4) = (x+5)//(Y+10)`

Options

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

Explanation

To solve the given equations step by step, we will start with the first equation and then move on to the second equation.

### Step 1: Solve the first equation
The first equation is given as:
\[ \frac{3x - 2}{y} = \frac{3x + 6}{y + 16} \]

Cross-multiply to eliminate the fractions:
\[ (3x - 2)(y + 16) = (3x + 6)y \]

Expanding both sides:
\[ 3xy + 48x - 2y - 32 = 3xy + 6y \]

Now, simplify by subtracting \(3xy\) from both sides:
\[ 48x - 2y - 32 = 6y \]

Rearranging gives:
\[ 48x - 32 = 6y + 2y \]
\[ 48x - 32 = 8y \]

Dividing the entire equation by 8:
\[ 6x - 4 = y \]

### Step 2: Solve the second equation
The second equation is:
\[ \frac{x + 2}{y + 4} = \frac{x + 5}{y + 10} \]

Cross-multiply:
\[ (x + 2)(y + 10) = (x + 5)(y + 4) \]

Expanding both sides:
\[ xy + 10x + 2y + 20 = xy + 4x + 5y + 20 \]

Now, simplify by subtracting \(xy\) and \(20\) from both sides:
\[ 10x + 2y = 4x + 5y \]

Rearranging gives:
\[ 10x - 4x = 5y - 2y \]
\[ 6x = 3y \]

Dividing the entire equation by 3:
\[ 2x = y \]

### Step 3: Substitute and solve for x and y
Now we have two equations:
1. \(y = 6x - 4\)
2. \(y = 2x\)

Setting the two expressions for \(y\) equal to each other:
\[ 6x - 4 = 2x \]

Rearranging gives:
\[ 6x - 2x = 4 \]
\[ 4x = 4 \]

Dividing by 4:
\[ x = 1 \]

Now substitute \(x = 1\) back into one of the equations to find \(y\):
Using \(y = 2x\):
\[ y = 2(1) = 2 \]

### Final Solution
Thus, the solution is:
\[ x = 1, \quad y = 2 \]