1. **State the problem:** Solve the system of equations using the substitution method: $$-x + 3y = -15$$ $$3x - y = 13$$ 2. **Choose one equation to solve for one variable:** From the first equation, solve for $x$: $$-x + 3y = -15 \implies -x = -15 - 3y \implies x = 15 + 3y$$ 3. **Substitute this expression for $x$ into the second equation:** $$3x - y = 13$$ $$3(15 + 3y) - y = 13$$ 4. **Simplify and solve for $y$:** $$45 + 9y - y = 13$$ $$45 + 8y = 13$$ 5. **Isolate $y$:** $$8y = 13 - 45$$ $$8y = -32$$ 6. **Divide both sides by 8:** $$y = \frac{-32}{8}$$ $$y = -4$$ 7. **Substitute $y = -4$ back into the expression for $x$:** $$x = 15 + 3(-4)$$ $$x = 15 - 12$$ $$x = 3$$ 8. **Check the solution $(x, y) = (3, -4)$ in both original equations:** First equation: $$-x + 3y = -15$$ $$-(3) + 3(-4) = -3 - 12 = -15$$ (True) Second equation: $$3x - y = 13$$ $$3(3) - (-4) = 9 + 4 = 13$$ (True) **Final answer:** $$\boxed{(3, -4)}$$