1. **State the problem:** Solve the system of equations using substitution: $$5x - 2y = -31$$ $$y = 2x + 13$$ 2. **Use substitution:** Since the second equation gives $y$ in terms of $x$, substitute $y = 2x + 13$ into the first equation. 3. **Substitute and simplify:** $$5x - 2(2x + 13) = -31$$ Distribute the $-2$: $$5x - 4x - 26 = -31$$ 4. **Combine like terms:** $$\cancel{5x} - \cancel{4x} - 26 = -31$$ Simplifies to: $$x - 26 = -31$$ 5. **Solve for $x$:** Add 26 to both sides: $$x - 26 + 26 = -31 + 26$$ $$x = -5$$ 6. **Find $y$ using $y = 2x + 13$:** $$y = 2(-5) + 13 = -10 + 13 = 3$$ **Final answer:** $$x = -5, \quad y = 3$$