1. **State the problem:** Solve the system of linear equations: $$3x + 3y = -6$$ $$7x + y = 22$$ 2. **Choose a method:** We will use substitution or elimination. Here, substitution is convenient. 3. **Isolate $y$ in the second equation:** $$7x + y = 22 \implies y = 22 - 7x$$ 4. **Substitute $y$ into the first equation:** $$3x + 3(22 - 7x) = -6$$ 5. **Simplify:** $$3x + 66 - 21x = -6$$ 6. **Combine like terms:** $$3x - 21x + 66 = -6$$ $$-18x + 66 = -6$$ 7. **Isolate $x$:** $$-18x = -6 - 66$$ $$-18x = -72$$ 8. **Divide both sides by $-18$:** $$x = \frac{-72}{-18}$$ $$x = \cancel{\frac{-72}{-18}} \Rightarrow x = 4$$ 9. **Substitute $x=4$ back into $y = 22 - 7x$:** $$y = 22 - 7(4)$$ $$y = 22 - 28$$ $$y = -6$$ **Final answer:** $$x = 4, \quad y = -6$$