1. **State the problem:** Solve the system of equations using the equal value method: $$3x + y = 8$$ $$2x + 5y = -25$$ 2. **Explain the equal value method:** This method involves solving both equations for the same variable and then setting those expressions equal to each other. 3. **Solve the first equation for $y$:** $$y = 8 - 3x$$ 4. **Solve the second equation for $y$:** $$2x + 5y = -25$$ $$5y = -25 - 2x$$ $$y = \frac{-25 - 2x}{5}$$ 5. **Set the two expressions for $y$ equal:** $$8 - 3x = \frac{-25 - 2x}{5}$$ 6. **Clear the denominator by multiplying both sides by 5:** $$5(8 - 3x) = -25 - 2x$$ $$40 - 15x = -25 - 2x$$ 7. **Bring all terms to one side:** $$40 + 25 = -2x + 15x$$ $$65 = 13x$$ 8. **Solve for $x$:** $$x = \frac{65}{13} = 5$$ 9. **Substitute $x=5$ back into $y = 8 - 3x$ to find $y$:** $$y = 8 - 3(5) = 8 - 15 = -7$$ 10. **Final answer:** $$x = 5, \quad y = -7$$