1. **State the problem:** Solve the system of linear equations: $$6x - 4y = 16$$ $$3x - 2y = 20$$ 2. **Use substitution or elimination method:** Here, notice the second equation is exactly half of the first equation's left side but not equal on the right side, so let's use elimination. 3. **Multiply the second equation by 2:** $$2(3x - 2y) = 2(20)$$ $$6x - 4y = 40$$ 4. **Compare with the first equation:** $$6x - 4y = 16$$ $$6x - 4y = 40$$ 5. **Subtract the first equation from the modified second equation:** $$(6x - 4y) - (6x - 4y) = 40 - 16$$ $$0 = 24$$ 6. **Since this is a contradiction, the system has no solution.** **Final answer:** The system is inconsistent and has no solution, so there is no pair $(x, y)$ that satisfies both equations.