1. **State the problem:** Solve the system of equations using elimination: $$9x + 6y = -12$$ $$7x + 6y = -8$$ 2. **Elimination method:** We want to eliminate one variable by subtracting the equations because the coefficients of $y$ are the same. 3. Subtract the second equation from the first: $$\left(9x + 6y\right) - \left(7x + 6y\right) = -12 - (-8)$$ 4. Simplify: $$9x - 7x + \cancel{6y} - \cancel{6y} = -12 + 8$$ $$2x = -4$$ 5. Solve for $x$: $$x = \frac{-4}{2} = -2$$ 6. Substitute $x = -2$ into the first equation to find $y$: $$9(-2) + 6y = -12$$ $$-18 + 6y = -12$$ 7. Add 18 to both sides: $$6y = -12 + 18$$ $$6y = 6$$ 8. Solve for $y$: $$y = \frac{6}{6} = 1$$ **Final answer:** $$(x, y) = (-2, 1)$$