1. **State the problem:** Solve the system of linear equations: $$x - 2y = 12$$ $$5x + 3y = -44$$ 2. **Use substitution or elimination method:** Here, we use substitution. From the first equation, express $x$ in terms of $y$: $$x - 2y = 12 \implies x = 12 + 2y$$ 3. **Substitute $x$ into the second equation:** $$5(12 + 2y) + 3y = -44$$ 4. **Simplify and solve for $y$:** $$60 + 10y + 3y = -44$$ $$60 + 13y = -44$$ $$13y = -44 - 60$$ $$13y = -104$$ $$y = \frac{-104}{13}$$ $$y = -8$$ 5. **Substitute $y = -8$ back into $x = 12 + 2y$ to find $x$:** $$x = 12 + 2(-8)$$ $$x = 12 - 16$$ $$x = -4$$ 6. **Final solution:** $$\boxed{(x, y) = (-4, -8)}$$ This means the two lines intersect at the point $(-4, -8)$.