1. **State the problem:** We are given the system of equations: $$2x + 3y = 7$$ $$x - y = 1$$ We need to find the value of $x + y$. 2. **Use substitution or elimination:** From the second equation, express $x$ in terms of $y$: $$x = y + 1$$ 3. **Substitute into the first equation:** $$2(y + 1) + 3y = 7$$ 4. **Simplify and solve for $y$:** $$2y + 2 + 3y = 7$$ $$5y + 2 = 7$$ $$5y = 7 - 2$$ $$5y = 5$$ $$y = \frac{5}{5}$$ $$y = 1$$ 5. **Find $x$ using $x = y + 1$:** $$x = 1 + 1 = 2$$ 6. **Calculate $x + y$:** $$x + y = 2 + 1 = 3$$ **Final answer:** $$\boxed{3}$$