1. **Solve the system:** $$\begin{cases} 2x - 3y = 2 \\ 3x + 2y = 16 \end{cases}$$ 2. **Elimination method:** Multiply the first equation by 2 and the second by 3 to align coefficients of $y$: $$\begin{cases} 2(2x - 3y) = 2 \times 2 \\ 3(3x + 2y) = 3 \times 16 \end{cases} \Rightarrow \begin{cases} 4x - 6y = 4 \\ 9x + 6y = 48 \end{cases}$$ 3. **Add the two equations to eliminate $y$:** $$ (4x - 6y) + (9x + 6y) = 4 + 48 \Rightarrow 13x = 52 $$ 4. **Solve for $x$:** $$ x = \frac{52}{13} = 4 $$ 5. **Substitute $x=4$ into the first original equation:** $$ 2(4) - 3y = 2 \Rightarrow 8 - 3y = 2 $$ 6. **Solve for $y$:** $$ -3y = 2 - 8 = -6 \Rightarrow y = \frac{-6}{-3} = 2 $$ **Final solution:** $\boxed{(x,y) = (4,2)}$