1. **State the problem:** Solve the system of equations: $$3x + 4y = 2$$ $$4x - 4y = 12$$ 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:** $$3x + 4y = 2$$ $$4x - 4y = 12$$ Adding gives: $$3x + 4y + 4x - 4y = 2 + 12$$ $$7x = 14$$ 4. **Solve for $x$:** $$x = \frac{14}{7} = 2$$ 5. **Substitute $x=2$ into the first equation:** $$3(2) + 4y = 2$$ $$6 + 4y = 2$$ 6. **Solve for $y$:** $$4y = 2 - 6 = -4$$ $$y = \frac{-4}{4} = -1$$ 7. **Final answer:** $$x = 2, \quad y = -1$$