1. **Problem statement:** Solve the first system of equations and find the value of $x+y$. 2. **Write the equations:** $$2x+3y=7$$ $$x-y=1$$ 3. **Use the second equation to express one variable:** From $x-y=1$, we get $$x=1+y$$ 4. **Substitute into the first equation:** $$2(1+y)+3y=7$$ $$2+2y+3y=7$$ $$2+5y=7$$ 5. **Solve for $y$:** $$5y=7-2$$ $$5y=5$$ $$\cancel{5}y=\cancel{5}$$ $$y=1$$ 6. **Find $x$:** $$x=1+y=1+1=2$$ 7. **Compute $x+y$:** $$x+y=2+1=3$$ 8. **Final answer:** $$\boxed{3}$$