1. **State the problem:** Solve the system of equations: $$\begin{aligned}&-3y+5x = 26 \\\ &-2y-5x = -16\end{aligned}$$ 2. **Add the two equations to eliminate $x$: ** $$(-3y + 5x) + (-2y - 5x) = 26 + (-16)$$ $$-3y + 5x - 2y - 5x = 10$$ $$-5y = 10$$ 3. **Solve for $y$: ** $$y = \frac{10}{-5}$$ $$y = -2$$ 4. **Substitute $y = -2$ into the first equation to solve for $x$: ** $$-3(-2) + 5x = 26$$ $$6 + 5x = 26$$ $$5x = 26 - 6$$ $$5x = 20$$ 5. **Solve for $x$: ** $$x = \frac{20}{5}$$ $$x = 4$$ **Final answer:** $$x = 4, \quad y = -2$$