`{{:(4x+3y=14-y),(x-5y=2):}`
If `(x,y)` is a solutin to the system of equations above, then what is the vaue of `x y `?

Options

A. `1/4`
B. 1
C. 3
D. 18

Explanation

To solve the system of equations given by:

1. \( 4x + 3y = 14 - y \)
2. \( x - 5y = 2 \)

we will follow these steps:

### Step 1: Rearranging the first equation
We start with the first equation:
\[ 4x + 3y = 14 - y \]
We can rearrange it by adding \( y \) to both sides:
\[ 4x + 3y + y = 14 \]
This simplifies to:
\[ 4x + 4y = 14 \]

### Step 2: Simplifying the first equation
Next, we can divide the entire equation by 4 to simplify:
\[ x + y = \frac{14}{4} \]
This simplifies to:
\[ x + y = \frac{7}{2} \]

### Step 3: Expressing x in terms of y
Now, we can express \( x \) in terms of \( y \):
\[ x = \frac{7}{2} - y \]

### Step 4: Substituting into the second equation
Now, we substitute \( x \) into the second equation:
\[ \left(\frac{7}{2} - y\right) - 5y = 2 \]
This simplifies to:
\[ \frac{7}{2} - 6y = 2 \]

### Step 5: Isolating y
Next, we isolate \( y \) by subtracting \( \frac{7}{2} \) from both sides:
\[ -6y = 2 - \frac{7}{2} \]
To simplify the right side, convert 2 to a fraction:
\[ 2 = \frac{4}{2} \]
Thus,
\[ -6y = \frac{4}{2} - \frac{7}{2} = -\frac{3}{2} \]
Now, dividing both sides by -6 gives:
\[ y = \frac{3}{12} = \frac{1}{4} \]

### Step 6: Finding x
Now that we have \( y \), we can find \( x \) using the expression we derived earlier:
\[ x = \frac{7}{2} - \frac{1}{4} \]
To perform this subtraction, convert \( \frac{7}{2} \) to a fraction with a denominator of 4:
\[ \frac{7}{2} = \frac{14}{4} \]
Thus,
\[ x = \frac{14}{4} - \frac{1}{4} = \frac{13}{4} \]

### Step 7: Finding the value of \( xy \)
Now we can find the product \( xy \):
\[ xy = \left(\frac{13}{4}\right) \left(\frac{1}{4}\right) = \frac{13}{16} \]

### Final Answer
The value of \( xy \) is:
\[ \frac{13}{16} \]