Find the value of x and y in the given equation `5 7/x xx y 1/13 = 12`:

Options

A. `-2,9`
B. `9, 2`
C. `4,3`
D. `9,4`

Answer

To solve the equation \( \frac{5 \cdot 7}{x \cdot y} \cdot \frac{1}{13} = 12 \), we will follow these steps:

### Step 1: Rewrite the equation
We start with the equation:
\[ \frac{5 \cdot 7}{x \cdot y} \cdot \frac{1}{13} = 12 \]
We can simplify the left side:
\[ \frac{35}{13xy} = 12 \]

### Step 2: Cross-multiply
Next, we cross-multiply to eliminate the fraction:
\[ 35 = 12 \cdot 13xy \]
This simplifies to:
\[ 35 = 156xy \]

### Step 3: Isolate \(xy\)
Now, we isolate \(xy\) by dividing both sides by 156:
\[ xy = \frac{35}{156} \]

### Step 4: Simplify the fraction
We can simplify \( \frac{35}{156} \):
- The greatest common divisor (GCD) of 35 and 156 is 1 (since 35 is 5 × 7 and 156 is 2 × 2 × 3 × 13).
Thus, \( \frac{35}{156} \) is already in its simplest form.

### Step 5: Find values for \(x\) and \(y\)
Now, we need to find pairs of \(x\) and \(y\) such that:
\[ xy = \frac{35}{156} \]
We can choose different values for \(x\) and calculate \(y\) accordingly. For example:
- If \(x = 1\), then \(y = \frac{35}{156} \approx 0.2244\)
- If \(x = 2\), then \(y = \frac{35}{312} \approx 0.1122\)
- If \(x = 5\), then \(y = \frac{35}{780} \approx 0.04487\)

### Conclusion
Thus, the values of \(x\) and \(y\) can vary as long as their product equals \( \frac{35}{156} \).