The problem asks us to solve a system of two linear equations for $x$ and $y$, and then find the value of $x + y$. The system of equations is: $3x - y = 7$ $5x + 9 = 25$

1. Problem Description

The problem asks us to solve a system of two linear equations for $x$ and $y$, and then find the value of $x + y$. The system of equations is:

$3x - y = 7$

$5x + 9 = 25$

2. Solution Steps

First, we solve the second equation for $x$:

$5x + 9 = 25$

$5x = 25 - 9$

$5x = 16$

$x = \frac{16}{5}$

Next, we substitute the value of $x$ into the first equation to solve for $y$:

$3x - y = 7$

$3(\frac{16}{5}) - y = 7$

$\frac{48}{5} - y = 7$

$-y = 7 - \frac{48}{5}$

$-y = \frac{35}{5} - \frac{48}{5}$

$-y = \frac{-13}{5}$

$y = \frac{13}{5}$

Now we calculate $x + y$:

$x + y = \frac{16}{5} + \frac{13}{5}$

$x + y = \frac{16 + 13}{5}$

$x + y = \frac{29}{5}$

3. Final Answer

$\frac{29}{5}$