1. **State the problem:** Solve the system of linear equations: $$x + y = -10$$ $$-3x - y = 2$$ 2. **Formula and rules:** We can solve this system using the method of addition (elimination) or substitution. Here, elimination is convenient because adding the two equations will eliminate $y$. 3. **Add the two equations:** $$\begin{aligned} &(x + y) + (-3x - y) = -10 + 2 \\ &x + y - 3x - y = -8 \\ &\cancel{x} + \cancel{y} - 3x - \cancel{y} = -8 \\ &-2x = -8 \end{aligned}$$ 4. **Solve for $x$:** $$\begin{aligned} -2x &= -8 \\ x &= \frac{-8}{-2} \\ x &= 4 \end{aligned}$$ 5. **Substitute $x=4$ into the first equation to find $y$:** $$\begin{aligned} 4 + y &= -10 \\ y &= -10 - 4 \\ y &= -14 \end{aligned}$$ 6. **Final answer:** $$\boxed{x=4, \quad y=-14}$$ This means the solution to the system is the point $(4, -14)$ where both equations intersect.