1. **Stating the problem:** Solve the system of linear equations using the substitution method: $$\begin{cases} 2x + 3y = 2 \\ 2x - 3y = 14 \end{cases}$$ 2. **Formula and rules:** The substitution method involves solving one equation for one variable and substituting that expression into the other equation. 3. **Step 1: Solve the first equation for $x$:** $$2x + 3y = 2 \implies 2x = 2 - 3y \implies x = \frac{2 - 3y}{2}$$ 4. **Step 2: Substitute $x$ into the second equation:** $$2\left(\frac{2 - 3y}{2}\right) - 3y = 14$$ Simplify: $$2 - 3y - 3y = 14$$ $$2 - 6y = 14$$ 5. **Step 3: Solve for $y$:** $$-6y = 14 - 2$$ $$-6y = 12$$ $$y = \frac{12}{-6} = -2$$ 6. **Step 4: Substitute $y = -2$ back into the expression for $x$:** $$x = \frac{2 - 3(-2)}{2} = \frac{2 + 6}{2} = \frac{8}{2} = 4$$ 7. **Final answer:** $$\boxed{(x, y) = (4, -2)}$$ This means the solution to the system is $x=4$ and $y=-2$.