1. **State the problem:** Solve the system of equations using elimination: $$\begin{cases} 3x + 2y = 8 \\ -3x + 2y = 8 \end{cases}$$ 2. **Explain the elimination method:** The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other. 3. **Add the two equations to eliminate $x$:** $$ (3x + 2y) + (-3x + 2y) = 8 + 8 $$ $$ 3x - 3x + 2y + 2y = 16 $$ $$ 0 + 4y = 16 $$ $$ 4y = 16 $$ 4. **Solve for $y$:** $$ y = \frac{16}{4} $$ $$ y = 4 $$ 5. **Substitute $y=4$ into the first equation to solve for $x$:** $$ 3x + 2(4) = 8 $$ $$ 3x + 8 = 8 $$ 6. **Isolate $x$:** $$ 3x = 8 - 8 $$ $$ 3x = 0 $$ $$ x = \frac{0}{3} $$ $$ x = 0 $$ **Final answer:** $$ x = 0, \quad y = 4 $$