1. **State the problem:** Solve the system of equations using elimination: $$\begin{cases} y - x = 28 \\ y + x = 156 \end{cases}$$ 2. **Explain the elimination method:** The goal is to add or subtract the equations to eliminate one variable, making it easier to solve for the other. 3. **Add the two equations:** $$ (y - x) + (y + x) = 28 + 156 $$ Simplify: $$ y - x + y + x = 184 $$ $$ 2y = 184 $$ 4. **Solve for $y$:** $$ y = \frac{184}{2} $$ Show cancellation: $$ y = \frac{\cancel{184}}{\cancel{2}} = 92 $$ 5. **Substitute $y=92$ into one of the original equations, for example $y - x = 28$:** $$ 92 - x = 28 $$ 6. **Solve for $x$:** $$ -x = 28 - 92 $$ $$ -x = -64 $$ Multiply both sides by $-1$: $$ x = 64 $$ 7. **Final answer:** $$ \boxed{(x, y) = (64, 92)} $$