1. **Problem statement:** Solve the first system of linear equations: $$\begin{cases} x + y = 3 \\ 2x + 3y = 7 \end{cases}$$ 2. **Method:** Use substitution or elimination to find $x$ and $y$. 3. **Step 1:** From the first equation, express $x$ in terms of $y$: $$x = 3 - y$$ 4. **Step 2:** Substitute $x = 3 - y$ into the second equation: $$2(3 - y) + 3y = 7$$ 5. **Step 3:** Simplify the equation: $$6 - 2y + 3y = 7$$ $$6 + y = 7$$ 6. **Step 4:** Solve for $y$: $$y = 7 - 6 = 1$$ 7. **Step 5:** Substitute $y = 1$ back into $x = 3 - y$: $$x = 3 - 1 = 2$$ 8. **Answer:** The solution to the system is: $$\boxed{(x, y) = (2, 1)}$$