If `(2x + 3y)/(3x - 4y) = (11)/(7),` then the value of `(x)/(y)` is _________.

Options

A. `65//19`
B. `68//19`
C. `67//19`
D. `64//19`

Answer

To solve the equation \(\frac{2x + 3y}{3x - 4y} = \frac{11}{7}\), we will follow these steps:

### Step 1: Cross-Multiply
We start by cross-multiplying to eliminate the fractions. This gives us:
\[ 7(2x + 3y) = 11(3x - 4y) \]

### Step 2: Distribute
Next, we distribute both sides:
\[ 14x + 21y = 33x - 44y \]

### Step 3: Rearrange the Equation
Now, we will rearrange the equation to get all terms involving \(x\) on one side and all terms involving \(y\) on the other side. We can do this by subtracting \(14x\) and adding \(44y\) to both sides:
\[ 21y + 44y = 33x - 14x \]
This simplifies to:
\[ 65y = 19x \]

### Step 4: Solve for \(\frac{x}{y}\)
Now, we can express \(\frac{x}{y}\) by dividing both sides by \(y\) and then by 19:
\[ \frac{x}{y} = \frac{65}{19} \]

Thus, the value of \(\frac{x}{y}\) is \(\frac{65}{19}\).

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