1. **State the problem:** Solve the system of equations: $$4x + 2y = 10$$ $$x - y = 13$$ 2. **Use substitution or elimination method:** Here, we use substitution. From the second equation, express $x$ in terms of $y$: $$x - y = 13 \implies x = y + 13$$ 3. **Substitute $x = y + 13$ into the first equation:** $$4(y + 13) + 2y = 10$$ 4. **Expand and simplify:** $$4y + 52 + 2y = 10$$ $$6y + 52 = 10$$ 5. **Isolate $y$:** $$6y = 10 - 52$$ $$6y = -42$$ 6. **Divide both sides by 6:** $$y = \frac{-42}{6}$$ $$y = \cancel{\frac{-42}{6}} = -7$$ 7. **Find $x$ using $x = y + 13$:** $$x = -7 + 13 = 6$$ **Final answer:** $$x = 6, \quad y = -7$$