If $3x-7y=14$ and $\frac{x}{x+y}=\frac{7}{9}$, then what is the value of $xy$?

Given equations:
1. $3x-7y=14$
2. $\frac{x}{x+y}=\frac{7}{9}$

From equation (2), perform cross-multiplication:

$$9x=7(x+y)$$

$$9x=7x+7y$$

$$2x=7y$$

Substitute $7y=2x$ into equation (1):

$$3x-2x=14$$

$$x=14$$

Now substitute $x=14$ back into the relation $2x=7y$ to find $y$:

$$2(14)=7y$$

$$28=7y$$

$$y=4$$

Now, evaluate the value of $xy$:

$$xy=14\times 4=56$$