1. **State the problem:** Solve the system of linear equations: $$x - 4y = 8$$ $$2x + y = -2$$ 2. **Choose a method:** We will use substitution or elimination. Here, substitution is straightforward. 3. **Isolate $x$ in the first equation:** $$x = 8 + 4y$$ 4. **Substitute $x$ into the second equation:** $$2(8 + 4y) + y = -2$$ 5. **Simplify and solve for $y$:** $$16 + 8y + y = -2$$ $$16 + 9y = -2$$ $$9y = -2 - 16$$ $$9y = -18$$ $$y = \frac{-18}{9}$$ $$y = -2$$ 6. **Substitute $y = -2$ back into $x = 8 + 4y$ to find $x$:** $$x = 8 + 4(-2)$$ $$x = 8 - 8$$ $$x = 0$$ 7. **Solution:** The system's solution is $$(x, y) = (0, -2)$$ 8. **Graphing explanation:** - The first line $x - 4y = 8$ can be rewritten as $y = \frac{x - 8}{4}$. - The second line $2x + y = -2$ can be rewritten as $y = -2x - 2$. - Plotting these lines on a graph, their intersection point is $(0, -2)$, which is the solution. This means the two lines cross exactly at that point.