1. **State the problem:** Solve the system of equations using elimination: $$-7x + 10y = 6$$ $$6x - 10y = 2$$ 2. **Explain elimination method:** The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other. 3. **Add the two equations to eliminate $y$:** $$(-7x + 10y) + (6x - 10y) = 6 + 2$$ 4. **Simplify the left side by canceling $10y$ and $-10y$:** $$-7x + \cancel{10y} + 6x - \cancel{10y} = 8$$ $$(-7x + 6x) = 8$$ 5. **Combine like terms:** $$-x = 8$$ 6. **Solve for $x$:** $$x = -8$$ 7. **Substitute $x = -8$ into one of the original equations to find $y$. Use the first equation:** $$-7(-8) + 10y = 6$$ $$56 + 10y = 6$$ 8. **Isolate $y$:** $$10y = 6 - 56$$ $$10y = -50$$ 9. **Divide both sides by 10:** $$\cancel{10}y = \frac{-50}{\cancel{10}}$$ $$y = -5$$ 10. **Final answer:** $$\boxed{(-8, -5)}$$