OpenSAT

To solve for $x+y$, we can multiply the first equation by 5 and the second equation by 7 to eliminate $y$. This gives us $15x + 35y = 70$ and $14x - 35y = 7$. Adding these equations together, we get $29x = 77$. Solving for $x$, we find $x=\frac{77}{29}$. Substituting this value of $x$ into the first equation, we get $3(\frac{77}{29})+7y=14$. Solving for $y$, we find $y=\frac{35}{29}$. Therefore, $x+y = \frac{77}{29} + \frac{35}{29} = \frac{112}{29} = 3\frac{25}{29}$.