1. **State the problem:** Solve the system of equations using elimination: $$\begin{cases} 2x + 3y = -2 \\ 3x - 6y = 18 \end{cases}$$ 2. **Elimination method:** We want to eliminate one variable by making the coefficients of either $x$ or $y$ the same (or opposites). 3. Multiply the first equation by 2 to align the $y$ coefficients: $$2(2x + 3y) = 2(-2) \Rightarrow 4x + 6y = -4$$ 4. Now the system is: $$\begin{cases} 4x + 6y = -4 \\ 3x - 6y = 18 \end{cases}$$ 5. Add the two equations to eliminate $y$: $$ (4x + 6y) + (3x - 6y) = -4 + 18 \Rightarrow 7x = 14 $$ 6. Solve for $x$: $$ x = \frac{14}{7} = 2 $$ 7. Substitute $x=2$ into the first original equation: $$ 2(2) + 3y = -2 \Rightarrow 4 + 3y = -2 $$ 8. Solve for $y$: $$ 3y = -2 - 4 = -6 \Rightarrow y = \frac{-6}{3} = -2 $$ **Final answer:** $$ (x, y) = (2, -2) $$