1. **State the problem:** Solve the system of linear equations: $$-2x + 6y = 6$$ $$-7x + 8y = -5$$ 2. **Choose a method:** We will use the elimination method to solve for $x$ and $y$. 3. **Eliminate one variable:** Multiply the first equation by 7 and the second by 2 to align coefficients of $x$: $$7(-2x + 6y) = 7(6) \Rightarrow -14x + 42y = 42$$ $$2(-7x + 8y) = 2(-5) \Rightarrow -14x + 16y = -10$$ 4. **Subtract the second from the first:** $$(-14x + 42y) - (-14x + 16y) = 42 - (-10)$$ $$-14x + 42y + 14x - 16y = 42 + 10$$ $$26y = 52$$ 5. **Solve for $y$:** $$y = \frac{52}{26} = 2$$ 6. **Substitute $y=2$ into the first original equation:** $$-2x + 6(2) = 6$$ $$-2x + 12 = 6$$ 7. **Solve for $x$:** $$-2x = 6 - 12$$ $$-2x = -6$$ $$x = \frac{-6}{-2} = 3$$ **Final answer:** $$x = 3, \quad y = 2$$