1. **State the problem:** Solve the system of equations: $$\begin{cases} x + y = 3 \\ x - y = -1 \end{cases}$$ 2. **Formula and rules:** To solve a system of linear equations, we can use the addition (elimination) method or substitution method. Here, elimination is straightforward. 3. **Add the two equations:** $$ (x + y) + (x - y) = 3 + (-1) $$ Simplify: $$ x + y + x - y = 2x = 2 $$ 4. **Solve for $x$:** $$ 2x = 2 \implies x = \frac{2}{2} = 1 $$ 5. **Substitute $x=1$ into the first equation:** $$ 1 + y = 3 \implies y = 3 - 1 = 2 $$ 6. **Final answer:** $$ x = 1, \quad y = 2 $$ This means the solution to the system is the point $(1, 2)$ where both equations intersect.