1. **State the problem:** Solve the system of linear equations for part (a): $$6x + 12y = -6$$ $$3x - 2y = -27$$ 2. **Choose a method:** We will use the substitution or elimination method. Here, elimination is convenient. 3. **Eliminate one variable:** Multiply the second equation by 6 to align coefficients of $x$: $$6 \times (3x - 2y) = 6 \times (-27)$$ $$18x - 12y = -162$$ 4. **Add the first equation and the new equation:** $$6x + 12y = -6$$ $$18x - 12y = -162$$ Add: $$6x + 12y + 18x - 12y = -6 - 162$$ $$ (6x + 18x) + (12y - 12y) = -168$$ $$24x + 0 = -168$$ $$24x = -168$$ 5. **Solve for $x$:** $$x = \frac{-168}{24}$$ $$x = \cancel{\frac{-168}{24}} = -7$$ 6. **Substitute $x = -7$ into the second original equation:** $$3(-7) - 2y = -27$$ $$-21 - 2y = -27$$ 7. **Solve for $y$:** $$-2y = -27 + 21$$ $$-2y = -6$$ $$y = \frac{-6}{-2}$$ $$y = 3$$ **Final answer:** $$x = -7, \quad y = 3$$ This completes the solution for part (a).