1. **State the problem:** Solve the system of linear equations: $$-3x - 2y = -18$$ $$3x + 3y = 12$$ 2. **Formula and rules:** We can solve this system using the elimination method by adding or subtracting equations to eliminate one variable. 3. **Add the two equations:** $$(-3x - 2y) + (3x + 3y) = -18 + 12$$ Simplify: $$\cancel{-3x} - 2y + \cancel{3x} + 3y = -6$$ $$y = -6$$ 4. **Substitute $y = -6$ into the first equation:** $$-3x - 2(-6) = -18$$ Simplify: $$-3x + 12 = -18$$ 5. **Isolate $x$:** $$-3x = -18 - 12$$ $$-3x = -30$$ Divide both sides by $-3$: $$x = \frac{-30}{-3}$$ $$x = 10$$ 6. **Final answer:** $$x = 10, \quad y = -6$$