1. **State the problem.** We need to solve the system $2x+3y=7$ and $x-y=1$, then find the value of $x+y$. 2. **Use the formula from the second equation.** From $x-y=1$, solve for one variable: $$x= y+1$$ 3. **Substitute into the first equation.** Replace $x$ in $2x+3y=7$ with $y+1$: $$2(y+1)+3y=7$$ 4. **Simplify step by step.** Distribute the $2$: $$2y+2+3y=7$$ Combine like terms: $$5y+2=7$$ Subtract $2$ from both sides: $$5y+\cancel{2}=7-\cancel{2}$$ $$5y=5$$ Divide both sides by $5$: $$\frac{\cancel{5y}}{\cancel{5}}=\frac{5}{5}$$ $$y=1$$ 5. **Find $x$.** Use $x=y+1$: $$x=1+1=2$$ 6. **Compute $x+y$.** $$x+y=2+1=3$$ 7. **Final answer.** The value of $x+y$ is $3$.