1. We are given the system of equations: $$\begin{cases} 2x + 3y = 2 \\ 2x - 3y = 14 \end{cases}$$ 2. To solve this system, we can add the two equations to eliminate $y$: $$ (2x + 3y) + (2x - 3y) = 2 + 14 $$ $$ 4x = 16 $$ 3. Solve for $x$: $$ x = \frac{16}{4} = 4 $$ 4. Substitute $x=4$ into the first equation to find $y$: $$ 2(4) + 3y = 2 $$ $$ 8 + 3y = 2 $$ $$ 3y = 2 - 8 = -6 $$ $$ y = \frac{-6}{3} = -2 $$ 5. The solution to the system is: $$ (x, y) = (4, -2) $$