1. **State the problem:** Solve the system of linear equations: $$3x + y = 8$$ $$2x + 5y = -25$$ 2. **Choose a method:** We will use the substitution or elimination method. Here, let's use substitution by solving the first equation for $y$. 3. **Solve for $y$ in the first equation:** $$y = 8 - 3x$$ 4. **Substitute $y$ into the second equation:** $$2x + 5(8 - 3x) = -25$$ 5. **Expand and simplify:** $$2x + 40 - 15x = -25$$ 6. **Combine like terms:** $$\cancel{2x} - 15x + 40 = -25$$ $$-13x + 40 = -25$$ 7. **Isolate $x$:** $$-13x = -25 - 40$$ $$-13x = -65$$ 8. **Divide both sides by $-13$:** $$x = \frac{-65}{-13} = 5$$ 9. **Substitute $x=5$ back into $y = 8 - 3x$:** $$y = 8 - 3(5) = 8 - 15 = -7$$ 10. **Final solution:** $$x = 5, \quad y = -7$$ This means the solution to the system is the point $(5, -7)$ where both equations intersect.