1. Problem: Solve the system of equations: $$\begin{cases} x + y = 10 \\ x - y = 2 \end{cases}$$ 2. Formula and rules: To solve a system of linear equations, we can use the addition (elimination) method or substitution method. Here, we use addition to eliminate $y$. 3. Add the two equations: $$ (x + y) + (x - y) = 10 + 2 $$ $$ 2x = 12 $$ 4. Solve for $x$: $$ x = \frac{12}{2} = 6 $$ 5. Substitute $x=6$ into the first equation: $$ 6 + y = 10 $$ $$ y = 10 - 6 = 4 $$ 6. Final answer: $$ x = 6, \quad y = 4 $$ This means the solution to the system is the point $(6,4)$ where both equations intersect.