1. **Stating the problem:** Solve the system of equations using substitution or elimination method: $$\begin{cases} 8x = 5y + 2 \\ 5 - 3x = -4y \end{cases}$$ 2. **Rewrite the equations in standard form:** From the first equation: $$8x = 5y + 2 \implies 8x - 5y = 2$$ From the second equation: $$5 - 3x = -4y \implies -3x + 4y = -5$$ 3. **Use elimination method:** Multiply the first equation by 4 and the second by 5 to align coefficients of $y$: $$4(8x - 5y) = 4(2) \implies 32x - 20y = 8$$ $$5(-3x + 4y) = 5(-5) \implies -15x + 20y = -25$$ 4. **Add the two equations to eliminate $y$:** $$ (32x - 20y) + (-15x + 20y) = 8 + (-25)$$ $$ (32x - 15x) + (-20y + 20y) = -17$$ $$17x + \cancel{0} = -17$$ 5. **Solve for $x$:** $$x = \frac{-17}{17} = -1$$ 6. **Substitute $x = -1$ into one of the original equations to find $y$:** Using $8x - 5y = 2$: $$8(-1) - 5y = 2$$ $$-8 - 5y = 2$$ $$-5y = 2 + 8 = 10$$ $$y = \frac{10}{-5} = -2$$ 7. **Final answer:** $$\boxed{x = -1, y = -2}$$