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