1. **State the problem:** Solve the system of equations: $$-4x - 4y = 7$$ $$4y - y = 2$$ 2. **Simplify the second equation:** $$4y - y = 3y$$ So the system becomes: $$-4x - 4y = 7$$ $$3y = 2$$ 3. **Solve for $y$ from the second equation:** $$y = \frac{2}{3}$$ 4. **Substitute $y = \frac{2}{3}$ into the first equation:** $$-4x - 4\left(\frac{2}{3}\right) = 7$$ 5. **Simplify:** $$-4x - \frac{8}{3} = 7$$ 6. **Add $\frac{8}{3}$ to both sides:** $$-4x = 7 + \frac{8}{3}$$ $$-4x = \frac{21}{3} + \frac{8}{3} = \frac{29}{3}$$ 7. **Divide both sides by $-4$:** $$x = \frac{\cancel{1}}{\cancel{-4}} \times \frac{29}{3} = -\frac{29}{12}$$ 8. **Final solution:** $$x = -\frac{29}{12}, \quad y = \frac{2}{3}$$