1. **State the problem:** Solve the system of equations: $$-3x + 6y = 9$$ $$5x + 7y = -49$$ 2. **Choose a method:** We will use the substitution or elimination method. Here, elimination is convenient. 3. **Eliminate one variable:** Multiply the first equation by 5 and the second by 3 to align coefficients of $x$: $$5(-3x + 6y) = 5(9) \Rightarrow -15x + 30y = 45$$ $$3(5x + 7y) = 3(-49) \Rightarrow 15x + 21y = -147$$ 4. **Add the two equations to eliminate $x$:** $$(-15x + 30y) + (15x + 21y) = 45 + (-147)$$ $$\cancel{-15x} + 30y + \cancel{15x} + 21y = -102$$ $$51y = -102$$ 5. **Solve for $y$:** $$y = \frac{-102}{51} = -2$$ 6. **Substitute $y = -2$ into one original equation to find $x$:** Using the first equation: $$-3x + 6(-2) = 9$$ $$-3x - 12 = 9$$ $$-3x = 9 + 12 = 21$$ $$x = \frac{21}{-3} = -7$$ 7. **Solution:** The solution to the system is $x = -7$, $y = -2$. 8. **Check the answer:** Substitute into the second equation: $$5(-7) + 7(-2) = -35 - 14 = -49$$ which is true. **Final answer:** $(-7, -2)$ which corresponds to option A.