1. **State the problem:** Solve the system of equations: $$2x + 3y = 54$$ $$2x - 4y = -16$$ 2. **Use the elimination method:** Subtract the second equation from the first to eliminate $x$: $$\cancel{2x} + 3y - (\cancel{2x} - 4y) = 54 - (-16)$$ $$3y + 4y = 54 + 16$$ $$7y = 70$$ 3. **Solve for $y$:** $$y = \frac{70}{7} = 10$$ 4. **Substitute $y=10$ into the first equation to find $x$:** $$2x + 3(10) = 54$$ $$2x + 30 = 54$$ $$2x = 54 - 30 = 24$$ $$x = \frac{24}{2} = 12$$ 5. **Final answer:** $$x = 12, \quad y = 10$$